具有区间不可微时变时滞的线性大系统分散指数稳定性的LMI方法

摘要

本文研究了一类互联中具有时变时滞的线性大系统的分散指数稳定性问题。时滞是属于给定区间的任何连续函数，但不一定是可微的。通过构造适当的增广Lyapunov-Krasovskii泛函并结合Leibniz-Newton公式，建立了基于LMI的分散指数稳定性存在的新的时滞相关充分条件。通过算例验证了所得结果的有效性。

1引言

泛函微分方程的理论和应用是现代非线性动力学的重要组成部分。这些方程是各种现实生活现象的自然数学模型，其中的后效是其功能的内在特征。近年来，泛函微分方程被用于模拟不同领域的过程，如人口动力学和生态学、生理学和医学、经济学以及其他自然科学。时变时滞线性系统的稳定性分析$\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="A">A类</trans>}\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="D">D类</trans>}\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="h">小时</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>$是许多实际问题的基础，受到了相当大的关注[1–4]. 关于这个问题的大多数已知结果都是假设时变时滞$\mathrm{<trans\; data-src="h">小时</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>$是一个连续可微函数，满足其导数的一些有界性条件：$\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="\le ">\le </trans>\mathrm{<trans\; data-src="\delta ">\delta </trans>}<trans\; data-src="<"><</trans>\mathrm{<trans\; data-src="1">1</trans>}$在时滞相关稳定性判据中，主要关注的是在给定的时滞区间内扩大稳定性判据的可行域。区间时变延迟是指时间延迟在一个区间内发生变化，在该区间内，下限不限于零。通过构造适当的增广Lyapunov泛函并利用自由权矩阵，在[5–10]对于时滞在区间内变化的系统。然而，这些工作中使用的方法的缺点是，假设延迟函数是微分的，并且其导数仍然有界：$\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="\le ">\le </trans>\mathrm{<trans\; data-src="\delta ">\delta </trans>}$.

另一方面，人们对大规模互联系统有着相当大的研究兴趣。典型的大规模互联系统，如电网，由许多子系统和单个元件连接在一起，形成一个大型复杂网络，能够在大的地理区域内发电、传输和分配电能。一般来说，大型系统的特征是代表系统的大量变量、子系统变量之间的强交互作用以及子系统之间的复杂交互作用。大规模互联动力系统的分散控制问题受到了广泛关注，因为在许多实际控制问题中存在大量大规模互联动力系，例如交通系统、电力系统、通信系统、经济系统、社会系统等[11–14]. 大规模互联系统的运行要求能够通过利用内部系统状态，在面临不确定性、干扰、故障和攻击时进行监控和稳定。然而，即使假设所有状态变量都可用于反馈控制，使用全局（集中式）状态反馈控制器有效控制大规模互联系统的任务仍然不容易，因为需要在子系统之间进行信息传输[15–18].

据我们所知，对子系统间相互作用的具有时变时滞的大系统的指数稳定性尚未进行过研究。事实上，这个问题很难解决；特别是当时变时滞是区间的、不可微的且输出服从这种时变时滞函数时。假设时滞是属于给定区间的任何连续函数，这意味着时变时滞的上下界是可用的，但时滞函数是有界的，但不一定是可微的。这使得时滞成为一个快速时变函数，且下限不限于零。显然，将任何无记忆反馈控制器应用于此类时滞系统都会导致具有区间时变时滞的闭环系统。当试图导出指数稳定性条件时，就会出现困难。事实上，现有的Lyapunov-Krasovskii功能和相关结果[11,14,15,18–35]不能用于解决本文提出的问题，因为它们要么无法处理延迟的不可微性，要么导致非常复杂的矩阵不等式条件，而矩阵计算或变量变换等技术都无法提取无记忆反馈控制器的参数。这激发了我们的研究。

本文考虑一类具有区间时变时滞的关联大系统。与现有结果相比，我们的结果有其自身的优势。（i） 以往文献的稳定性分析揭示了一些限制：时滞被认为是时不变的相互关联的，或者时滞下限被限制为零，或者时滞函数应该是微分的且其导数是有界的。我们的结果是，对于大规模系统，去掉了上述限制条件。此外，假设时滞是属于给定区间的任何连续函数，这意味着时变时滞的上下界是可用的，但时滞函数是有界的，但不一定是可微的。这使得时延成为一个快速时变函数，并且下界不限于零。（ii）所开发的方法使用了新的下界交叉项不等式，消除了过界的需要，并提供了更大的允许延迟界值。我们提出了一组新的Lyapunov-Krasovskii泛函，这些泛函主要基于上下界的信息。（iii）条件将以LMI的解的形式给出，该解可以通过使用标准计算算法以有效的方式进行数值求解[36].

论文组织如下。第2节给出了证明主要结果所需的定义和一些众所周知的技术命题。第3节给出了大系统分散指数稳定性的主要结果。第4节给出了数值示例，说明了所得结果的有效性。本文最后给出了结论和引用的参考文献。

2准备工作

本文使用了以下符号。${\mathrm{<trans\; data-src="R">R（右）</trans>}}^{<trans\; data-src="+">+</trans>}$表示所有实数非负数的集合；${\mathrm{<trans\; data-src="R">R（右）</trans>}}^{\mathrm{<trans\; data-src="n">n个</trans>}}$表示n个-具有标量积的维空间$<trans\; data-src="〈">〈</trans><trans\; data-src="\cdot ">\cdot </trans><trans\; data-src=",">,</trans><trans\; data-src="\cdot ">\cdot </trans><trans\; data-src="〉">〉</trans>$和向量范数$<trans\; data-src="\parallel ">\parallel </trans><trans\; data-src="\cdot ">\cdot </trans>\parallel$；${\mathrm{<trans\; data-src="M">M（M）</trans>}}^{\mathrm{<trans\; data-src="n">n个</trans>}<trans\; data-src="\times ">\times </trans>\mathrm{<trans\; data-src="r">对</trans>}}$表示的所有矩阵的空间$<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="n">n个</trans>}<trans\; data-src="\times ">\times </trans>\mathrm{<trans\; data-src="r">对</trans>}<trans\; data-src=")">)</trans>$-维度；${\mathrm{<trans\; data-src="A">A类</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}$表示矩阵的转置A类；A类对称，如果$\mathrm{<trans\; data-src="A">A类</trans>}<trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="A">A类</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}$；我表示单位矩阵；$\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="A">A类</trans>}<trans\; data-src=")">)</trans>$表示所有特征值的集合A类；${\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="min">最小值</trans>}<trans\; data-src="/">/</trans>\mathrm{<trans\; data-src="max">最大值</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="A">A类</trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="min">最小值</trans>}<trans\; data-src="/">/</trans>\mathrm{<trans\; data-src="max">最大值</trans>}<trans\; data-src="\{">\{</trans><trans\; data-src="Re">重新</trans>\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}<trans\; data-src=";">；</trans>\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}<trans\; data-src="\in ">\in </trans>\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="A">A类</trans>}<trans\; data-src=")">)</trans><trans\; data-src="\}">\}</trans>$；${\mathrm{<trans\; data-src="C">C类</trans>}}^{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="(">(</trans><trans\; data-src="[">[</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="b">b条</trans>}<trans\; data-src="]">]</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}^{\mathrm{<trans\; data-src="n">n个</trans>}}<trans\; data-src=")">)</trans>$表示全部的集合${\mathrm{<trans\; data-src="R">R（右）</trans>}}^{\mathrm{<trans\; data-src="n">n个</trans>}}$-上的值可微函数$<trans\; data-src="[">[</trans>\mathrm{<trans\; data-src="a">一</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="b">b条</trans>}<trans\; data-src="]">]</trans>$；${\mathrm{<trans\; data-src="L">L（左）</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="(">(</trans><trans\; data-src="[">[</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\infty ">\infty </trans>}<trans\; data-src="]">]</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}^{\mathrm{<trans\; data-src="r">对</trans>}}<trans\; data-src=")">)</trans>$代表全平方积分集${\mathrm{<trans\; data-src="R">R（右）</trans>}}^{\mathrm{<trans\; data-src="r">对</trans>}}$-上的值函数$<trans\; data-src="[">[</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\infty ">\infty </trans>}<trans\; data-src="]">]</trans>$.${\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="t">t吨</trans>}}<trans\; data-src=":">:</trans><trans\; data-src="=">=</trans><trans\; data-src="\{">\{</trans>\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans><trans\; data-src=":">:</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src="\in ">\in </trans><trans\; data-src="[">[</trans><trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="h">小时</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src="]">]</trans><trans\; data-src="\}">\}</trans>$,$<trans\; data-src="\parallel ">\parallel </trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="t">t吨</trans>}}<trans\; data-src="\parallel ">\parallel </trans><trans\; data-src="=">=</trans>{<trans\; data-src="sup">啜饮</trans>}_{\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src="\in ">\in </trans><trans\; data-src="[">[</trans><trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="h">小时</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src="]">]</trans>}<trans\; data-src="\parallel ">\parallel </trans>\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans><trans\; data-src="\parallel ">\parallel </trans>$；$\mathrm{<trans\; data-src="C">C类</trans>}<trans\; data-src="(">(</trans><trans\; data-src="[">[</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="]">]</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}^{\mathrm{<trans\; data-src="n">n个</trans>}}<trans\; data-src=")">)</trans>$表示全部的集合${\mathrm{<trans\; data-src="R">R（右）</trans>}}^{\mathrm{<trans\; data-src="n">n个</trans>}}$-上的值连续函数$<trans\; data-src="[">[</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="]">]</trans>$; 矩阵A类称为半正定($\mathrm{<trans\; data-src="A">A类</trans>}<trans\; data-src="\ge ">\ge </trans>\mathrm{<trans\; data-src="0">0</trans>}$)如果$<trans\; data-src="〈">〈</trans>\mathrm{<trans\; data-src="A">A类</trans>}\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="〉">〉</trans><trans\; data-src="\ge ">\ge </trans>\mathrm{<trans\; data-src="0">0</trans>}$为所有人$\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="\in ">\in </trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}^{\mathrm{<trans\; data-src="n">n个</trans>}}$；A类是正定的($\mathrm{<trans\; data-src="A">A类</trans>}<trans\; data-src=">">></trans>\mathrm{<trans\; data-src="0">0</trans>}$)如果$<trans\; data-src="〈">〈</trans>\mathrm{<trans\; data-src="A">A类</trans>}\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="〉">〉</trans><trans\; data-src=">">></trans>\mathrm{<trans\; data-src="0">0</trans>}$为所有人$\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="0">0</trans>}$；$\mathrm{<trans\; data-src="A">A类</trans>}<trans\; data-src=">">></trans>\mathrm{<trans\; data-src="B">B类</trans>}$方法$\mathrm{<trans\; data-src="A">A类</trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="B">B类</trans>}<trans\; data-src=">">></trans>\mathrm{<trans\; data-src="0">0</trans>}$.∗表示矩阵中的对称项。

考虑一类具有区间时变时滞的线性大系统，该系统由N个互联子系统$\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="=">=</trans>\stackrel{<trans\; data-src="¯">¯</trans>}{\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="N">N个</trans>}}$表单的

$$\begin{array}{r}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="+">+</trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\in ">\in </trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}^{<trans\; data-src="+">+</trans>}<trans\; data-src=",">,</trans>\\ {\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="\phi ">\phi </trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\forall ">\forall </trans>}\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\in ">\in </trans><trans\; data-src="[">[</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src="]">]</trans><trans\; data-src=",">,</trans>\end{array}$$

(2.1)

哪里${\mathrm{<trans\; data-src="x">x个</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans><trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans><trans\; data-src="\dots ">\dots </trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="N">N个</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="]">]</trans>$,${\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="\in ">\in </trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}^{{\mathrm{<trans\; data-src="n">n个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}}$，是状态向量，系统矩阵${\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}$,${\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}$具有适当的尺寸。

时间延迟${\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans><trans\; data-src="\cdot ">\cdot </trans><trans\; data-src=")">)</trans>$连续并满足以下条件：

$$\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src="\le ">\le </trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="\le ">\le </trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="<"><</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\ge ">\ge </trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\forall ">\forall </trans>}\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\stackrel{<trans\; data-src="¯">¯</trans>}{\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="N">N个</trans>}}<trans\; data-src=",">,</trans>$$

和初始函数$\mathrm{<trans\; data-src="\phi ">\phi </trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans><trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="\phi ">\phi </trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans><trans\; data-src="\dots ">\dots </trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="\phi ">\phi </trans>}}_{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="]">]</trans>$,${\mathrm{<trans\; data-src="\phi ">\phi </trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="\in ">\in </trans>{\mathrm{<trans\; data-src="C">C类</trans>}}^{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="(">(</trans><trans\; data-src="[">[</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src="]">]</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}^{{\mathrm{<trans\; data-src="n">n个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}}<trans\; data-src=")">)</trans>$，符合标准

$$<trans\; data-src="\parallel ">\parallel </trans>{\mathrm{<trans\; data-src="\phi ">\phi </trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="\parallel ">\parallel </trans><trans\; data-src="=">=</trans>\underset{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="h">小时</trans>}<trans\; data-src="\le ">\le </trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\le ">\le </trans>\mathrm{<trans\; data-src="0">0</trans>}}{<trans\; data-src="sup">啜饮</trans>}<trans\; data-src="\{">\{</trans><trans\; data-src="\parallel ">\parallel </trans>{\mathrm{<trans\; data-src="\phi ">\phi </trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="\parallel ">\parallel </trans><trans\; data-src=",">,</trans><trans\; data-src="\parallel ">\parallel </trans>{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="\phi ">\phi </trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="\parallel ">\parallel </trans><trans\; data-src="\}">\}</trans><trans\; data-src=",">,</trans><trans\; data-src="\parallel ">\parallel </trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}<trans\; data-src="\parallel ">\parallel </trans><trans\; data-src="=">=</trans>\sqrt{\underset{\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\parallel {\mathrm{<trans\; data-src="\phi ">\phi </trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="\parallel ">\parallel </trans>}^{\mathrm{<trans\; data-src="2">2</trans>}}}<trans\; data-src=".">.</trans>$$

定义2.1鉴于$\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}<trans\; data-src=">">></trans>\mathrm{<trans\; data-src="0">0</trans>}$系统（2.1）的零解为α-存在正数时指数稳定$\mathrm{<trans\; data-src="N">N个</trans>}<trans\; data-src=">">></trans>\mathrm{<trans\; data-src="0">0</trans>}$这样每个解决方案$\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}<trans\; data-src=")">)</trans>$满足以下条件：

$$<trans\; data-src="\parallel ">\parallel </trans>\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}<trans\; data-src=")">)</trans><trans\; data-src="\parallel ">\parallel </trans><trans\; data-src="\le ">\le </trans>\mathrm{<trans\; data-src="N">N个</trans>}{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}\mathrm{<trans\; data-src="t">t吨</trans>}}<trans\; data-src="\parallel ">\parallel </trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}<trans\; data-src="\parallel ">\parallel </trans><trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\forall ">\forall </trans>}\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\in ">\in </trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}^{<trans\; data-src="+">+</trans>}<trans\; data-src=".">.</trans>$$

我们以以下技术上众所周知的命题结束本节，这些命题将用于证明主要结果。

提议2.1 对于任何 $\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="y">年</trans>}<trans\; data-src="\in ">\in </trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}^{\mathrm{<trans\; data-src="n">n个</trans>}}$ 和正定矩阵 $\mathrm{<trans\; data-src="P">对</trans>}<trans\; data-src="\in ">\in </trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}^{\mathrm{<trans\; data-src="n">n个</trans>}<trans\; data-src="\times ">\times </trans>\mathrm{<trans\; data-src="n">n个</trans>}}$,我们有

$$\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}\mathrm{<trans\; data-src="y">年</trans>}<trans\; data-src="\le ">\le </trans>{\mathrm{<trans\; data-src="y">年</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}\mathrm{<trans\; data-src="P">对</trans>}\mathrm{<trans\; data-src="y">年</trans>}<trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="P">对</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="1">1</trans>}}\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src=".">.</trans>$$

提议2.2（Schur补引理[37])

给定常数矩阵 X（X）,Y（Y）,Z轴 适当尺寸满足 $\mathrm{<trans\; data-src="X">X（X）</trans>}<trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="X">X（X）</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="Y">Y（Y）</trans>}<trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="Y">Y（Y）</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src=">">></trans>\mathrm{<trans\; data-src="0">0</trans>}$.然后 $\mathrm{<trans\; data-src="X">X（X）</trans>}<trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="Z">Z轴</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="Y">Y（Y）</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="1">1</trans>}}\mathrm{<trans\; data-src="Z">Z轴</trans>}<trans\; data-src="<"><</trans>\mathrm{<trans\; data-src="0">0</trans>}$ 当且仅当

$$<trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="X">X（X）</trans>}& {\mathrm{<trans\; data-src="Z">Z轴</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}\\ \mathrm{<trans\; data-src="Z">Z轴</trans>}& <trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="Y">Y（Y）</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src="<"><</trans>\mathrm{<trans\; data-src="0">0</trans>}\mathit{\text{<trans data-src="or">或</trans>}}<trans\; data-src="(">(</trans>\begin{array}{cc}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="Y">Y（Y）</trans>}& \mathrm{<trans\; data-src="Z">Z轴</trans>}\\ {\mathrm{<trans\; data-src="Z">Z轴</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}& \mathrm{<trans\; data-src="X">X（X）</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src="<"><</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=".">.</trans>$$

提议2.3[38]

对于任何常量矩阵 $\mathrm{<trans\; data-src="Z">Z轴</trans>}<trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="Z">Z轴</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src=">">></trans>\mathrm{<trans\; data-src="0">0</trans>}$ 和标量 小时,$\stackrel{<trans\; data-src="¯">¯</trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}$,$\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src="<"><</trans>\mathrm{<trans\; data-src="h">小时</trans>}<trans\; data-src="<"><</trans>\stackrel{<trans\; data-src="¯">¯</trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}$ 这样就可以很好地定义以下集成,然后

$$\begin{array}{c}<trans\; data-src="-">负极</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="h">小时</trans>}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}\mathrm{<trans\; data-src="x">x个</trans>}{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}\mathrm{<trans\; data-src="Z">Z轴</trans>}\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src="\le ">\le </trans><trans\; data-src="-">负极</trans>\frac{\mathrm{<trans\; data-src="1">1</trans>}}{\mathrm{<trans\; data-src="h">小时</trans>}}{<trans\; data-src="(">(</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="h">小时</trans>}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}\mathrm{<trans\; data-src="Z">Z轴</trans>}<trans\; data-src="(">(</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="h">小时</trans>}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\hfill \\ <trans\; data-src="-">负极</trans>{<trans\; data-src="\int ">\int </trans>}_{<trans\; data-src="-">负极</trans>\stackrel{<trans\; data-src="¯">¯</trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="h">小时</trans>}}{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}\mathrm{<trans\; data-src="x">x个</trans>}{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}\mathrm{<trans\; data-src="Z">Z轴</trans>}\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}\hfill \\ <trans\; data-src="\le ">\le </trans><trans\; data-src="-">负极</trans>\frac{\mathrm{<trans\; data-src="2">2</trans>}}{{\stackrel{<trans\; data-src="¯">¯</trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}}{<trans\; data-src="(">(</trans>{<trans\; data-src="\int ">\int </trans>}_{<trans\; data-src="-">负极</trans>\stackrel{<trans\; data-src="¯">¯</trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="h">小时</trans>}}{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}\mathrm{<trans\; data-src="Z">Z轴</trans>}<trans\; data-src="(">(</trans>{<trans\; data-src="\int ">\int </trans>}_{<trans\; data-src="-">负极</trans>\stackrel{<trans\; data-src="¯">¯</trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="h">小时</trans>}}{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans><trans\; data-src=".">.</trans>\hfill \end{array}$$

3主要成果

在本节中，我们研究了具有区间时变时滞的线性大系统（2.1）的分散指数稳定性。从下面的定理可以看出，在我们的推导中既没有使用自由加权矩阵，也没有使用任何变换。在介绍主要结果之前，为了简单起见，定义了几个矩阵变量的以下符号

$$\begin{array}{c}\begin{array}{rl}{\mathrm{<trans\; data-src="M">M（M）</trans>}}_{\mathrm{<trans\; data-src="11">11</trans>}}^{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="=">=</trans>& {\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}\\ <trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="1">1</trans>}}{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}\\ <trans\; data-src="-">负极</trans><trans\; data-src="(">(</trans>\frac{\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="4">4</trans>}\mathrm{<trans\; data-src="\beta ">\beta </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}}{{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}}<trans\; data-src=")">)</trans>{<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="2">2</trans>}}{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; 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data-src="N">N个</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="3">三</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="3">三</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="M">M（M）</trans>}}_{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="N">N个</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}<trans\; data-src=")">)</trans><trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="N">N个</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="3">三</trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="3">三</trans>}}<trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="M">M（M）</trans>}}_{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="N">N个</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}<trans\; data-src=")">)</trans><trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="N">N个</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="4">4</trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=",">,</trans>\hfill \\ \begin{array}{rl}{\mathrm{<trans\; data-src="M">M（M）</trans>}}_{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="N">N个</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="3">三</trans>}<trans\; data-src=")">)</trans><trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="N">N个</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="3">三</trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="=">=</trans>& <trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="5">5</trans>}}<trans\; data-src="+">+</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}\\ <trans\; data-src="+">+</trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="5">5</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="5">5</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src=",">,</trans>\end{array}\hfill \\ {\mathrm{<trans\; data-src="M">M（M）</trans>}}_{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="N">N个</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="3">三</trans>}<trans\; data-src=")">)</trans><trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="N">N个</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="4">4</trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="M">M（M）</trans>}}_{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="N">N个</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="4">4</trans>}<trans\; data-src=")">)</trans><trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="N">N个</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="4">4</trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\frac{\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="4">4</trans>}\mathrm{<trans\; data-src="\beta ">\beta </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}}{{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="min">最小值</trans>}}<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="=">=</trans>\underset{\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="=">=</trans>\stackrel{<trans\; data-src="¯">¯</trans>}{\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="N">N个</trans>}}}{<trans\; data-src="min">最小值</trans>}{\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="=">=</trans>\underset{\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="=">=</trans>\stackrel{<trans\; data-src="¯">¯</trans>}{\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="N">N个</trans>}}}{<trans\; data-src="max">最大值</trans>}{\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=",">,</trans>\hfill \\ \begin{array}{rl}{\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="=">=</trans>& {\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="max">最大值</trans>}}<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="max">最大值</trans>}}<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="3">三</trans>}}{\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="max">最大值</trans>}}<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans>{<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="3">三</trans>}}{\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="max">最大值</trans>}}<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="+">+</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}{\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="max">最大值</trans>}}<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src=")">)</trans><trans\; data-src=".">.</trans>\end{array}\hfill \end{array}$$

以下是本文的主要结果，它给出了具有区间时变时滞的线性大系统（2.1）的分散指数稳定性的充分条件。本质上，该证明基于满足时滞系统Lyapunov稳定性定理的Lyapunov-Krasovskii函数的构造[37].

定理3.1 鉴于 $\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}<trans\; data-src=">">></trans>\mathrm{<trans\; data-src="0">0</trans>}$.系统(2.1)是 α-存在对称正定矩阵时指数稳定 ${\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}$,${\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}$,${\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}$,${\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}$,${\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}$,$\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="=">=</trans>\stackrel{<trans\; data-src="¯">¯</trans>}{\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="N">N个</trans>}}$,和矩阵 ${\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}$,$\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="=">=</trans>\stackrel{<trans\; data-src="¯">¯</trans>}{\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="N">N个</trans>}}$,$\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="2">2</trans>}<trans\; data-src=",">,</trans><trans\; data-src="\dots ">\dots </trans><trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="5">5</trans>}$,以下LMI保持不变:

$${\mathcal{<trans\; data-src="M">M（M）</trans>}}^{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="[">[</trans>\begin{array}{cccc}{\mathrm{<trans\; data-src="M">M（M）</trans>}}_{\mathrm{<trans\; data-src="11">11</trans>}}^{\mathrm{<trans\; data-src="i">我</trans>}}& {\mathrm{<trans\; data-src="M">M（M）</trans>}}_{\mathrm{<trans\; data-src="12">12</trans>}}^{\mathrm{<trans\; data-src="i">我</trans>}}& <trans\; data-src="\cdots ">\cdots </trans>& {\mathrm{<trans\; data-src="M">M（M）</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="N">N个</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="4">4</trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="i">我</trans>}}\\ <trans\; data-src="\ast ">\ast </trans>& {\mathrm{<trans\; data-src="M">M（M）</trans>}}_{\mathrm{<trans\; data-src="22">22</trans>}}^{\mathrm{<trans\; data-src="i">我</trans>}}& <trans\; data-src="\cdots ">\cdots </trans>& {\mathrm{<trans\; data-src="M">M（M）</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="N">N个</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="4">4</trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="i">我</trans>}}\\ <trans\; data-src="\cdot ">\cdot </trans>& <trans\; data-src="\cdot ">\cdot </trans>& <trans\; data-src="\cdots ">\cdots </trans>& <trans\; data-src="\cdot ">\cdot </trans>\\ <trans\; data-src="\ast ">\ast </trans>& <trans\; data-src="\ast ">\ast </trans>& <trans\; data-src="\cdots ">\cdots </trans>& {\mathrm{<trans\; data-src="M">M（M）</trans>}}_{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="N">N个</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="4">4</trans>}<trans\; data-src=")">)</trans><trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="N">N个</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="4">4</trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="i">我</trans>}}\end{array}<trans\; data-src="]">]</trans><trans\; data-src="<"><</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="=">=</trans>\stackrel{<trans\; data-src="¯">¯</trans>}{\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="N">N个</trans>}}<trans\; data-src=".">.</trans>$$

(3.1)

此外,解决方案 $\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}<trans\; data-src=")">)</trans>$ 系统满足

$$<trans\; data-src="\parallel ">\parallel </trans>\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}<trans\; data-src=")">)</trans><trans\; data-src="\parallel ">\parallel </trans><trans\; data-src="\le ">\le </trans>\sqrt{\frac{{\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{{\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}}{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}\mathrm{<trans\; data-src="t">t吨</trans>}}<trans\; data-src="\parallel ">\parallel </trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}<trans\; data-src="\parallel ">\parallel </trans><trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\forall ">\forall </trans>}\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\in ">\in </trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}^{<trans\; data-src="+">+</trans>}<trans\; data-src=".">.</trans>$$

证明我们考虑系统（2.1）的以下Lyapunov-Krasovskii函数：

$$\mathrm{<trans\; data-src="V">V（V）</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="t">t吨</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>\underset{\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="7">7</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="t">t吨</trans>}}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>$$

哪里

$$\begin{array}{c}{\mathrm{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="=">=</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="3">三</trans>}}<trans\; data-src="=">=</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="4">4</trans>}}<trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}{<trans\; data-src="\int ">\int </trans>}_{<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}^{\mathrm{<trans\; data-src="0">0</trans>}}{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="s">秒</trans>}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\tau ">\tau </trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\tau ">\tau </trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\tau ">\tau </trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\tau ">\tau </trans>}\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="5">5</trans>}}<trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}{<trans\; data-src="\int ">\int </trans>}_{<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="0">0</trans>}}{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="s">秒</trans>}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\tau ">\tau </trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\tau ">\tau </trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\tau ">\tau </trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\tau ">\tau </trans>}\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="6">6</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{<trans\; data-src="\int ">\int </trans>}_{<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="s">秒</trans>}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\tau ">\tau </trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\tau ">\tau </trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\tau ">\tau </trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\tau ">\tau </trans>}\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="7">7</trans>}}<trans\; data-src="=">=</trans>{<trans\; data-src="\int ">\int </trans>}_{<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="\theta ">\theta </trans>}}^{\mathrm{<trans\; data-src="0">0</trans>}}{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="s">秒</trans>}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\tau ">\tau </trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\tau ">\tau </trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\tau ">\tau </trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\tau ">\tau </trans>}\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=".">.</trans>\hfill \end{array}$$

很容易验证

$$\underset{\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="1">1</trans>}}{<trans\; data-src="\parallel ">\parallel </trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="\parallel ">\parallel </trans>}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="\le ">\le </trans>\mathrm{<trans\; data-src="V">V（V）</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="t">t吨</trans>}}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="V">V（V）</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="0">0</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="\le ">\le </trans>\underset{\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="2">2</trans>}}{<trans\; data-src="\parallel ">\parallel </trans>{\mathrm{<trans\; data-src="\phi ">\phi </trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="\parallel ">\parallel </trans>}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=".">.</trans>$$

(3.2)

求…的导数V（V）在里面t吨沿着系统（2.1）的解，我们有

$$\begin{array}{c}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\hfill \\ \phantom{{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="1">1</trans>}}}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="]">]</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src=";">；</trans>\hfill \\ {\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=";">；</trans>\hfill \\ {\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="3">三</trans>}}<trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="3">三</trans>}}<trans\; data-src=";">；</trans>\hfill \\ {\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="4">4</trans>}}<trans\; data-src="\le ">\le </trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="4">4</trans>}}<trans\; data-src=";">；</trans>\hfill \\ {\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="5">5</trans>}}<trans\; data-src="\le ">\le </trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="5">5</trans>}}<trans\; data-src=";">；</trans>\hfill \\ {\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="6">6</trans>}}<trans\; data-src="\le ">\le </trans>{<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="2">2</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\hfill \\ \phantom{{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="6">6</trans>}}<trans\; data-src="\le ">\le </trans>}<trans\; data-src="-">负极</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="6">6</trans>}}<trans\; data-src=";">；</trans>\hfill \\ {\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="7">7</trans>}}<trans\; data-src="\le ">\le </trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\hfill \\ \phantom{{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="7">7</trans>}}<trans\; data-src="\le ">\le </trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="4">4</trans>}\mathrm{<trans\; data-src="\beta ">\beta </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{<trans\; data-src="\int ">\int </trans>}_{<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="7">7</trans>}}<trans\; data-src=".">.</trans>\hfill \end{array}$$

应用命题2.3和Leibniz-Newton公式

$${<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="h">小时</trans>}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="h">小时</trans>}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>$$

我们有

$$\begin{array}{rl}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}& <trans\; data-src="\le ">\le </trans><trans\; data-src="-">负极</trans>{<trans\; data-src="[">[</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src="]">]</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="[">[</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src="]">]</trans>\\ <trans\; data-src="\le ">\le </trans><trans\; data-src="-">负极</trans>{<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="]">]</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="]">]</trans>\\ <trans\; data-src="=">=</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="R">R（右）</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src=")">)</trans><trans\; data-src=".">.</trans>\end{array}$$

请注意

$${<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src="=">=</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src="+">+</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=".">.</trans>$$

使用命题2.3给出

$$\begin{array}{r}<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="]">]</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}\\ <trans\; data-src="\ge ">\ge </trans>{<trans\; data-src="[">[</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src="]">]</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="[">[</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src="]">]</trans>\\ <trans\; data-src="\ge ">\ge </trans>{<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="]">]</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="]">]</trans><trans\; data-src=".">.</trans>\end{array}$$

自${\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="\le ">\le </trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}$，我们有

$$\begin{array}{r}<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="]">]</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}\\ <trans\; data-src="\ge ">\ge </trans>{<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="]">]</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="]">]</trans><trans\; data-src=",">,</trans>\end{array}$$

然后

$$\begin{array}{r}<trans\; data-src="-">负极</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}\\ <trans\; data-src="\le ">\le </trans><trans\; data-src="-">负极</trans>{<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="]">]</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="]">]</trans><trans\; data-src=".">.</trans>\end{array}$$

同样，我们有

$$\begin{array}{r}<trans\; data-src="-">负极</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}\\ <trans\; data-src="\le ">\le </trans><trans\; data-src="-">负极</trans>{<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="]">]</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="]">]</trans><trans\; data-src=".">.</trans>\end{array}$$

请注意，当${\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}$或${\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}$，我们有

$${<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="]">]</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="0">0</trans>}\text{<trans data-src="or">或</trans>}<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="]">]</trans><trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">,</trans>$$

分别是。此外，再次使用命题2.3，我们有

$$\begin{array}{r}{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="4">4</trans>}\mathrm{<trans\; data-src="\beta ">\beta </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{<trans\; data-src="\int ">\int </trans>}_{<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}\\ <trans\; data-src="\le ">\le </trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="4">4</trans>}\mathrm{<trans\; data-src="\beta ">\beta </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}\frac{\mathrm{<trans\; data-src="2">2</trans>}}{{\stackrel{<trans\; data-src="¯">¯</trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}}{<trans\; data-src="(">(</trans>{<trans\; data-src="\int ">\int </trans>}_{<trans\; data-src="-">负极</trans>\stackrel{<trans\; data-src="¯">¯</trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="h">小时</trans>}}{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}\mathrm{<trans\; data-src="Z">Z轴</trans>}<trans\; data-src="(">(</trans>{<trans\; data-src="\int ">\int </trans>}_{<trans\; data-src="-">负极</trans>\stackrel{<trans\; data-src="¯">¯</trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="h">小时</trans>}}{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}}^{\mathrm{<trans\; data-src="t">t吨</trans>}}\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="s">秒</trans>}\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>\\ <trans\; data-src="\le ">\le </trans>\frac{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="4">4</trans>}\mathrm{<trans\; data-src="\beta ">\beta </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}}{{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}}{<trans\; data-src="(">(</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}\\ <trans\; data-src="\times ">\times </trans>{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans><trans\; data-src=".">.</trans>\end{array}$$

因此，

$$\begin{array}{rl}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="7">7</trans>}}<trans\; data-src="\le ">\le </trans>& <trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="7">7</trans>}}<trans\; data-src="-">负极</trans>\frac{\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="4">4</trans>}\mathrm{<trans\; data-src="\beta ">\beta </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}}{{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}}{<trans\; data-src="(">(</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}\\ <trans\; data-src="\times ">\times </trans>{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans><trans\; data-src=".">.</trans>\end{array}$$

因此，我们有

$$\begin{array}{rl}\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}<trans\; data-src="(">(</trans><trans\; data-src="\cdot ">\cdot </trans><trans\; data-src=")">)</trans><trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}\mathrm{<trans\; data-src="V">V（V）</trans>}<trans\; data-src="(">(</trans><trans\; data-src="\cdot ">\cdot </trans><trans\; data-src=")">)</trans><trans\; data-src="\le ">\le </trans>& {\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="]">]</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>\\ <trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="+">+</trans>{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="[">[</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="]">]</trans>{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\\ <trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="]">]</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="]">]</trans>\\ <trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="]">]</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="]">]</trans>\\ <trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="]">]</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="]">]</trans>\\ <trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="]">]</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="]">]</trans>\\ <trans\; data-src="-">负极</trans>\frac{\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="4">4</trans>}\mathrm{<trans\; data-src="\beta ">\beta </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}}{{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}}{<trans\; data-src="(">(</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\\ <trans\; data-src="-">负极</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=".">.</trans>\end{array}$$

(3.3)

通过使用以下标识关系：

$${\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">,</trans>$$

我们有

$$\begin{array}{r}\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="1">1</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="1">1</trans>}}{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="1">1</trans>}}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">,</trans>\\ \mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="2">2</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="2">2</trans>}}{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="2">2</trans>}}\underset{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">,</trans>\\ \mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="3">三</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="3">三</trans>}}{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\\ <trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="3">三</trans>}}\underset{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">,</trans>\\ \mathrm{<trans\; data-src="2">2</trans>}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="4">4</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="4">4</trans>}}{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\\ <trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="4">4</trans>}}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">,</trans>\\ \mathrm{<trans\; data-src="2">2</trans>}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="5">5</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="5">5</trans>}}{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="5">5</trans>}}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=".">.</trans>\end{array}$$

(3.4)

将（3.4）的所有零项加到（3.3）中，我们得到

$$\begin{array}{rl}\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}<trans\; data-src="(">(</trans><trans\; data-src="\cdot ">\cdot </trans><trans\; data-src=")">)</trans><trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}\mathrm{<trans\; data-src="V">V（V）</trans>}<trans\; data-src="(">(</trans><trans\; data-src="\cdot ">\cdot </trans><trans\; data-src=")">)</trans><trans\; data-src="\le ">\le </trans>& {\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="1">1</trans>}}{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}\\ <trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="-">负极</trans><trans\; data-src="(">(</trans>\frac{\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="4">4</trans>}\mathrm{<trans\; data-src="\beta ">\beta </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}}{{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}}<trans\; data-src=")">)</trans>{<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="2">2</trans>}}{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="]">]</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="1">1</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="4">4</trans>}}{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="]">]</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="[">[</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="]">]</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="[">[</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="]">]</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans>{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="[">[</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="5">5</trans>}}<trans\; data-src="+">+</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="]">]</trans>{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="[">[</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="]">]</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; 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data-src="(">(</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="[">[</trans><trans\; data-src="(">(</trans>\frac{\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="4">4</trans>}\mathrm{<trans\; data-src="\beta ">\beta </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}}{{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="]">]</trans><trans\; data-src="(">(</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="[">[</trans><trans\; data-src="(">(</trans>\frac{\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="4">4</trans>}\mathrm{<trans\; data-src="\beta ">\beta </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}}{{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}}<trans\; data-src=")">)</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="]">]</trans><trans\; data-src="(">(</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans><trans\; data-src=".">.</trans>\end{array}$$

应用命题2.1，我们得到

$$\begin{array}{r}\begin{array}{rl}\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="\le ">\le </trans>& \underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\end{array}\\ \begin{array}{rl}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="1">1</trans>}}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="\le ">\le </trans>& \underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="1">1</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\end{array}\\ \begin{array}{rl}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="5">5</trans>}}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="\le ">\le </trans>& \underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="5">5</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="5">5</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\end{array}\\ <trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="3">三</trans>}}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="\le ">\le </trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="3">三</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="3">三</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\\ \phantom{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="3">三</trans>}}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="\le ">\le </trans>}<trans\; data-src="+">+</trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\\ <trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="4">4</trans>}}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>\\ <trans\; data-src="\le ">\le </trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="4">4</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="4">4</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\\ \begin{array}{rl}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="2">2</trans>}}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="\le ">\le </trans>& \underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="2">2</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="2">2</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\end{array}\\ \begin{array}{rl}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="4">4</trans>}}{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="\le ">\le </trans>& {\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="4">4</trans>}}{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="4">4</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src=".">.</trans>\end{array}\end{array}$$

(3.5)

因此，应用不等式（3.5）并注意到

$$\begin{array}{c}\underset{\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>\underset{\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}<trans\; data-src="[">[</trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="j">j个</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="]">]</trans><trans\; data-src=",">,</trans>\hfill \\ \underset{\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="a">一</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>\underset{\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}<trans\; data-src="[">[</trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="j">j个</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="a">一</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="]">]</trans><trans\; data-src=",">,</trans>\hfill \end{array}$$

我们有

$$\begin{array}{r}\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}<trans\; data-src="(">(</trans><trans\; data-src="\cdot ">\cdot </trans><trans\; data-src=")">)</trans><trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}\mathrm{<trans\; data-src="V">V（V）</trans>}<trans\; data-src="(">(</trans><trans\; data-src="\cdot ">\cdot </trans><trans\; data-src=")">)</trans>\\ <trans\; data-src="\le ">\le </trans>\underset{\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}<trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="1">1</trans>}}{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}\\ <trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="-">负极</trans><trans\; data-src="(">(</trans>\frac{\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="4">4</trans>}\mathrm{<trans\; data-src="\beta ">\beta </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}}{{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}}<trans\; data-src=")">)</trans>{<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="2">2</trans>}}{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}\\ <trans\; data-src="+">+</trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="1">1</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="4">4</trans>}}{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="4">4</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="]">]</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="[">[</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="2">2</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="2">2</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="]">]</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="[">[</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans>\underset{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="3">三</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="3">三</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="]">]</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans>{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="[">[</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="+">+</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; 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data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>\\ <trans\; data-src="-">负极</trans>{<trans\; data-src="(">(</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="[">[</trans><trans\; data-src="(">(</trans>\frac{\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="4">4</trans>}\mathrm{<trans\; data-src="\beta ">\beta </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}}{{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="]">]</trans><trans\; data-src="(">(</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>\\ <trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="[">[</trans><trans\; data-src="(">(</trans>\frac{\mathrm{<trans\; data-src="2">2</trans>}{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="4">4</trans>}\mathrm{<trans\; data-src="\beta ">\beta </trans>}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}}{{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}}<trans\; data-src=")">)</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="]">]</trans><trans\; data-src="(">(</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans><trans\; data-src="]">]</trans>\\ <trans\; data-src="=">=</trans>\underset{\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}{\overset{\mathrm{<trans\; data-src="N">N个</trans>}}{<trans\; data-src="\sum ">\sum </trans>}}{\mathrm{<trans\; data-src="\zeta ">\zeta </trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>{\mathcal{<trans\; data-src="M">M（M）</trans>}}^{\mathrm{<trans\; data-src="i">我</trans>}}{\mathrm{<trans\; data-src="\zeta ">\zeta </trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\end{array}$$

哪里${\mathrm{<trans\; data-src="\zeta ">\zeta </trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans><trans\; data-src="[">[</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>{<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="j">j个</trans>}\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>}_{\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="j">j个</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="N">N个</trans>}}<trans\; data-src=",">,</trans>{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>{<trans\; data-src="\int ">\int </trans>}_{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}^{\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}^{\mathrm{<trans\; data-src="T">T型</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="d">d日</trans>}\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src="]">]</trans>$.

根据条件（3.1），我们得到

$$\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="V">V（V）</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="t">t吨</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="\le ">\le </trans><trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}\mathrm{<trans\; data-src="V">V（V）</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="t">t吨</trans>}}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\forall ">\forall </trans>}\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\in ">\in </trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}^{<trans\; data-src="+">+</trans>}<trans\; data-src=".">.</trans>$$

(3.6)

将（3.6）的两侧从0积分到t吨，我们获得

$$\mathrm{<trans\; data-src="V">V（V）</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="t">t吨</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="\le ">\le </trans>\mathrm{<trans\; data-src="V">V（V）</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}\mathrm{<trans\; data-src="t">t吨</trans>}}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\forall ">\forall </trans>}\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\in ">\in </trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}^{<trans\; data-src="+">+</trans>}<trans\; data-src=".">.</trans>$$

此外，考虑到条件（3.2），我们有

$${\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}{<trans\; data-src="\parallel ">\parallel </trans>\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}<trans\; data-src=")">)</trans><trans\; data-src="\parallel ">\parallel </trans>}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="\le ">\le </trans>\mathrm{<trans\; data-src="V">V（V）</trans>}<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="t">t吨</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="\le ">\le </trans>\mathrm{<trans\; data-src="V">V（V）</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}<trans\; data-src=")">)</trans>{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}\mathrm{<trans\; data-src="t">t吨</trans>}}<trans\; data-src="\le ">\le </trans>{\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}\mathrm{<trans\; data-src="t">t吨</trans>}}{<trans\; data-src="\parallel ">\parallel </trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}<trans\; data-src="\parallel ">\parallel </trans>}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=",">,</trans>$$

然后

$$<trans\; data-src="\parallel ">\parallel </trans>\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}<trans\; data-src=")">)</trans><trans\; data-src="\parallel ">\parallel </trans><trans\; data-src="\le ">\le </trans>\sqrt{\frac{{\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{{\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}}}{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}\mathrm{<trans\; data-src="t">t吨</trans>}}<trans\; data-src="\parallel ">\parallel </trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}<trans\; data-src="\parallel ">\parallel </trans><trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\in ">\in </trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}^{<trans\; data-src="+">+</trans>}<trans\; data-src=".">.</trans>$$

这就完成了定理的证明。□

备注3.1定理3.1根据线性矩阵不等式的解为线性大系统（2.1）提供了充分条件，从而保证闭环系统在规定的衰减率下指数稳定α所开发的对较低边界交叉项使用新不等式的方法消除了对超边界的需要，并且提供了更大的容许延迟界值。注意，时变时滞是不可微的；因此[11,14,15,18–35]不适用于系统（2.1）。LMI条件（3.2）取决于所考虑系统的参数以及延迟界。LMI的可行性可以通过可靠高效的Matlab LMI控制工具箱进行测试[36].

4数值示例

在本节中，我们给出了一个数值例子来证明所提结果的有效性。

示例4.1本示例是一个由两个机器子系统组成的大型模型，如下所示：

$$\begin{array}{c}{\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="12">12</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="12">12</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\in ">\in </trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}^{<trans\; data-src="+">+</trans>}<trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="\phi ">\phi </trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\forall ">\forall </trans>}\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\in ">\in </trans><trans\; data-src="[">[</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src="]">]</trans><trans\; data-src=",">,</trans>\hfill \\ {\stackrel{<trans\; data-src="\dot{}">\dot{}</trans>}{\mathrm{<trans\; data-src="x">x个</trans>}}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="21">21</trans>}}{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="21">21</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\in ">\in </trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}^{<trans\; data-src="+">+</trans>}<trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>{\mathrm{<trans\; data-src="\phi ">\phi </trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\forall ">\forall </trans>}\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\in ">\in </trans><trans\; data-src="[">[</trans><trans\; data-src="-">负极</trans>{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src="]">]</trans><trans\; data-src=",">,</trans>\hfill \end{array}$$

其中，每个子系统中机器的绝对转子角和角速度表示为${\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="11">11</trans>}}<trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="12">12</trans>}}<trans\; data-src=")">)</trans>$和${\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="21">21</trans>}}<trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="22">22</trans>}}<trans\; data-src=")">)</trans>$分别为；这个我th系统系数${\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}$; 传递导纳模${\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}$; 初始输入${\mathrm{<trans\; data-src="\phi ">\phi </trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}$; 时变时滞${\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}\mathrm{<trans\; data-src="j">j个</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>$在子系统中的两台机器之间：

$$\begin{array}{c}{\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="12">12</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="\{">\{</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.1">0.1</trans>}<trans\; data-src="+">+</trans>{<trans\; data-src="sin">罪</trans>}^{\mathrm{<trans\; data-src="2">2</trans>}}\mathrm{<trans\; data-src="t">t吨</trans>}\hfill & \text{<trans data-src="if ">如果</trans>}\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\in ">\in </trans>\mathcal{<trans\; data-src="I">我</trans>}<trans\; data-src="=">=</trans>{<trans\; data-src="\bigcup ">\bigcup </trans>}_{\mathrm{<trans\; data-src="k">k个</trans>}<trans\; data-src="\ge ">\ge </trans>\mathrm{<trans\; data-src="0">0</trans>}}<trans\; data-src="[">[</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="k">k个</trans>}\mathrm{<trans\; data-src="\pi ">\pi </trans>}<trans\; data-src=",">,</trans><trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="k">k个</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="\pi ">\pi </trans>}<trans\; data-src="]">]</trans><trans\; data-src=",">,</trans>\hfill \\ \mathrm{<trans\; data-src="0.1">0.1</trans>}\hfill & \text{<trans data-src="if ">如果</trans>}\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\in ">\in </trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}^{<trans\; data-src="+">+</trans>}<trans\; data-src="\setminus ">\setminus </trans>\mathcal{<trans\; data-src="I">我</trans>}<trans\; data-src=",">,</trans>\hfill \end{array}\hfill \\ {\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="21">21</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="\{">\{</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.2">0.2</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="1.1">1.1</trans>}{<trans\; data-src="sin">罪</trans>}^{\mathrm{<trans\; data-src="2">2</trans>}}\mathrm{<trans\; data-src="t">t吨</trans>}\hfill & \text{<trans data-src="if ">如果</trans>}\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\in ">\in </trans>\mathcal{<trans\; data-src="I">我</trans>}<trans\; data-src="=">=</trans>{<trans\; data-src="\bigcup ">\bigcup </trans>}_{\mathrm{<trans\; data-src="k">k个</trans>}<trans\; data-src="\ge ">\ge </trans>\mathrm{<trans\; data-src="0">0</trans>}}<trans\; data-src="[">[</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="k">k个</trans>}\mathrm{<trans\; data-src="\pi ">\pi </trans>}<trans\; data-src=",">,</trans><trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="k">k个</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=")">)</trans>\mathrm{<trans\; data-src="\pi ">\pi </trans>}<trans\; data-src="]">]</trans><trans\; data-src=",">,</trans>\hfill \\ \mathrm{<trans\; data-src="0.2">0.2</trans>}\hfill & \text{<trans data-src="if ">如果</trans>}\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\in ">\in </trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}^{<trans\; data-src="+">+</trans>}<trans\; data-src="\setminus ">\setminus </trans>\mathcal{<trans\; data-src="I">我</trans>}<trans\; data-src=",">,</trans>\hfill \end{array}\hfill \\ {\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="1">1</trans>}& \mathrm{<trans\; data-src="0.5">0.5</trans>}\\ \mathrm{<trans\; data-src="1">1</trans>}& <trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="12">12</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="0.1">0.1</trans>}& \mathrm{<trans\; data-src="0.2">0.2</trans>}\\ \mathrm{<trans\; data-src="0.3">0.3</trans>}& <trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="0.5">0.5</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="A">A类</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="2">2</trans>}& \mathrm{<trans\; data-src="0.5">0.5</trans>}\\ \mathrm{<trans\; data-src="1">1</trans>}& <trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="3">三</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="D">D类</trans>}}_{\mathrm{<trans\; data-src="21">21</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="0.4">0.4</trans>}& \mathrm{<trans\; data-src="0.1">0.1</trans>}\\ \mathrm{<trans\; data-src="0.2">0.2</trans>}& <trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="0.3">0.3</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=".">.</trans>\hfill \end{array}$$

延迟起作用是毫无价值的${\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="12">12</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>$,${\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="21">21</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>$不可微；因此，中的方法[11,14,15,18–35]不适用于此系统。在Matlab中使用LMI工具箱[36]，LMI（3.1）适用于${\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="0.1">0.1</trans>}$,${\mathrm{<trans\; data-src="h">小时</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="1.3">1.3</trans>}$,$\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="0.1">0.1</trans>}$、和

$$\begin{array}{c}{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.2429">0.2429</trans>}& \mathrm{<trans\; data-src="0.0170">0.0170</trans>}\\ \mathrm{<trans\; data-src="0.0170">0.0170</trans>}& \mathrm{<trans\; data-src="0.4891">0.4891</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="P">对</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.4872">0.4872</trans>}& \mathrm{<trans\; data-src="0.2139">0.2139</trans>}\\ \mathrm{<trans\; data-src="0.2139">0.2139</trans>}& \mathrm{<trans\; data-src="0.7821">0.7821</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.7338">0.7338</trans>}& <trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="0.0014">0.0014</trans>}\\ <trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="0.0014">0.0014</trans>}& \mathrm{<trans\; data-src="0.7032">0.7032</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="Q">问</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.5110">0.5110</trans>}& <trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="0.0082">0.0082</trans>}\\ <trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="0.0082">0.0082</trans>}& \mathrm{<trans\; data-src="0.8108">0.8108</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.3724">0.3724</trans>}& \mathrm{<trans\; data-src="0.0329">0.0329</trans>}\\ \mathrm{<trans\; data-src="0.0329">0.0329</trans>}& \mathrm{<trans\; data-src="0.8680">0.8680</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.5001">0.5001</trans>}& \mathrm{<trans\; data-src="0.0881">0.0881</trans>}\\ \mathrm{<trans\; data-src="0.0881">0.0881</trans>}& \mathrm{<trans\; data-src="0.4892">0.4892</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.3486">0.3486</trans>}& \mathrm{<trans\; data-src="0.0149">0.0149</trans>}\\ \mathrm{<trans\; data-src="0.0149">0.0149</trans>}& \mathrm{<trans\; data-src="0.5664">0.5664</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="U">U型</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.7790">0.7790</trans>}& \mathrm{<trans\; data-src="0.2919">0.2919</trans>}\\ \mathrm{<trans\; data-src="0.2919">0.2919</trans>}& \mathrm{<trans\; data-src="0.5091">0.5091</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.3486">0.3486</trans>}& \mathrm{<trans\; data-src="0.0149">0.0149</trans>}\\ \mathrm{<trans\; data-src="0.0149">0.0149</trans>}& \mathrm{<trans\; data-src="0.5664">0.5664</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="W">W公司</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.7721">0.7721</trans>}& \mathrm{<trans\; data-src="0.0128">0.0128</trans>}\\ \mathrm{<trans\; data-src="0.0128">0.0128</trans>}& \mathrm{<trans\; data-src="0.6901">0.6901</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="11">11</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.8136">0.8136</trans>}& \mathrm{<trans\; data-src="0.0213">0.0213</trans>}\\ \mathrm{<trans\; data-src="0.0422">0.0422</trans>}& \mathrm{<trans\; data-src="0.4275">0.4275</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="21">21</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.5390">0.5390</trans>}& \mathrm{<trans\; data-src="0.0329">0.0329</trans>}\\ \mathrm{<trans\; data-src="0.0219">0.0219</trans>}& \mathrm{<trans\; data-src="0.6092">0.6092</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="12">12</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.3957">0.3957</trans>}& \mathrm{<trans\; data-src="0.0643">0.0643</trans>}\\ \mathrm{<trans\; data-src="0.0643">0.0643</trans>}& \mathrm{<trans\; data-src="1.3682">1.3682</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="22">22</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.7230">0.7230</trans>}& \mathrm{<trans\; data-src="0.0532">0.0532</trans>}\\ \mathrm{<trans\; data-src="0.0332">0.0332</trans>}& \mathrm{<trans\; data-src="0.9011">0.9011</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="13">13</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.3957">0.3957</trans>}& \mathrm{<trans\; data-src="0.0643">0.0643</trans>}\\ \mathrm{<trans\; data-src="0.0643">0.0643</trans>}& \mathrm{<trans\; data-src="1.3682">1.3682</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="23">23</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.5419">0.5419</trans>}& \mathrm{<trans\; data-src="0.0084">0.0084</trans>}\\ \mathrm{<trans\; data-src="0.0432">0.0432</trans>}& \mathrm{<trans\; data-src="0.8932">0.8932</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="14">14</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.3957">0.3957</trans>}& \mathrm{<trans\; data-src="0.0643">0.0643</trans>}\\ \mathrm{<trans\; data-src="0.0643">0.0643</trans>}& \mathrm{<trans\; data-src="1.3682">1.3682</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="24">24</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.4499">0.4499</trans>}& \mathrm{<trans\; data-src="0.0772">0.0772</trans>}\\ \mathrm{<trans\; data-src="0.03490">0.03490</trans>}& \mathrm{<trans\; data-src="0.5419">0.5419</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>\hfill \\ {\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="15">15</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.3957">0.3957</trans>}& \mathrm{<trans\; data-src="0.0643">0.0643</trans>}\\ \mathrm{<trans\; data-src="0.0643">0.0643</trans>}& \mathrm{<trans\; data-src="1.3682">1.3682</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="S">S公司</trans>}}_{\mathrm{<trans\; data-src="25">25</trans>}}<trans\; data-src="=">=</trans><trans\; data-src="(">(</trans>\begin{array}{cc}\mathrm{<trans\; data-src="0.9837">0.9837</trans>}& \mathrm{<trans\; data-src="0.04428">0.04428</trans>}\\ \mathrm{<trans\; data-src="0.0095">0.0095</trans>}& \mathrm{<trans\; data-src="0.9321">0.9321</trans>}\end{array}<trans\; data-src=")">)</trans><trans\; data-src=".">.</trans>\hfill \end{array}$$

根据定理3.1，系统是指数稳定的。最后，解决方案$\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}<trans\; data-src=")">)</trans>$系统满足

$$<trans\; data-src="\parallel ">\parallel </trans>\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}<trans\; data-src=")">)</trans><trans\; data-src="\parallel ">\parallel </trans><trans\; data-src="\le ">\le </trans>\mathrm{<trans\; data-src="19.2419">19.2419</trans>}{\mathrm{<trans\; data-src="e">电子</trans>}}^{<trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="0.1">0.1</trans>}\mathrm{<trans\; data-src="t">t吨</trans>}}<trans\; data-src="\parallel ">\parallel </trans>\mathrm{<trans\; data-src="\phi ">\phi </trans>}<trans\; data-src="\parallel ">\parallel </trans><trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\forall ">\forall </trans>}\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src="\in ">\in </trans>{\mathrm{<trans\; data-src="R">R（右）</trans>}}^{<trans\; data-src="+">+</trans>}<trans\; data-src=".">.</trans>$$

图1显示了${\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>$和${\mathrm{<trans\; data-src="x">x个</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans>$具有初始条件的闭环系统${\mathrm{<trans\; data-src="\phi ">\phi </trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans><trans\; data-src="[">[</trans>\mathrm{<trans\; data-src="2">2</trans>}\mathrm{<trans\; data-src="5">5</trans>}<trans\; data-src="]">]</trans>$,${\mathrm{<trans\; data-src="\phi ">\phi </trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="t">t吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans><trans\; data-src="[">[</trans><trans\; data-src="-">负极</trans>\mathrm{<trans\; data-src="3">三</trans>}\mathrm{<trans\; data-src="3">三</trans>}<trans\; data-src="]">]</trans>$.

图1

线性大系统解的轨迹。

线性大系统解的轨迹如图所示1分别是。

5结论

本文研究了大规模时变时滞系统的分散指数稳定性问题。假定时滞是属于给定区间的函数，但不一定是可微的。通过将适当的Lyapunov泛函、Newton-Leibniz公式和自由加权参数矩阵有效地结合起来，利用线性矩阵不等式导出了指数稳定性的新的时滞相关条件，它允许同时计算表征解的指数稳定率的两个界。所开发的方法使用了新的下界交叉项不等式，消除了过界的需要，并提供了更大的延迟界值。数值算例表明了所得结果的有效性。