一类中立型时滞系统的实用稳定性研究

The Practical Stability of a Class of Neutral Systems with Time-Delay

作者: 专业:运筹学与控制论 导师:卜春霞 年度:2010 学位:硕士  院校: 郑州大学

Keywords

neutral system, linear matrix inequations(LMIs), singularly system, practical stability

        中立型时滞系统的研究是近几十年来控制领域的一个热点,受到人们的日益关注.对这类不但包含过去的运动状态,还包含过去运动状态的微分信息的系统的研究具有重要的理论意义和应用价值.近年来,对中立型时滞系统的研究为人们解决相应的实际问题提供了良好的理论基础和方法.本论文基于LMI方法,在总结和归纳了现有方法的基础上,对中立型时滞系统的实用稳定性问题进行了深入的研究和分析.主要内容如下:首先:研究了一类带不确定项的中立型时滞系统的实用稳定性.利用线性矩阵不等式的处理方法和Lyapunov稳定性理论,得到了相应系统实用稳定的充分条件.其次,研究了时变的中立型时滞系统的实用稳定.时变的时滞项增加了研究的复杂性,通过对时变时滞的限制:得到了相应系统实用稳定的时滞相关,时滞变化率相关的充分条件.最后,通过构造广义的Lyapunov函数,研究了广义的时滞系统的实用稳定性条件.
    The study of the time-delay systems of neutral type became a hot issue and had attracted more and more researchers.The study of these systems,which contain not only information of the past state but also information of the derivative of the past state has important theoretical significance and application value. Recently,the study of the neutral systems has offered better theoretical basic and means for dealing with practice.In this paper,the problem of practical stability for neutral delay systems based on LMIs are deeply investigated and analyzed on the ground of the summarization of the popular methods.The main works are organized as following:Firstly, the problem of practical stability for a class of neutral delay system with uncertainties is studied. A sufficient condition for the practical stability of the system is derived on the basis of Lyapunov stability theory and linear matrix inequalities method.Secondly, the practical stability for a class of neutral delay system with time-varying delay is discussed. In this situation, the time-varying delay increases the complexity of the research. so a sufficient condition is presented for the system through limiting the time-varying delay.Finally, we have studied the practical stability for the singularly system with time-delay by constructing Lyapunov function and linear matrix inequalities approach.
        

一类中立型时滞系统的实用稳定性研究

摘要4-5
Abstract5
第一章 绪论7-17
    1.1 时滞系统的研究背景7-8
    1.2 中立型时滞系统的研究背景8-9
    1.3 什么是实用稳定性9-14
    1.4 预备知识14-16
    1.5 本文的主要研究内容16-17
第二章 不确定的中立型时滞系统的实用稳定性17-24
    2.1 标称系统的实用稳定性17-20
    2.2 含不确定项的中立型时滞系统的实用稳定性20-24
第三章 时变的中立型时滞系统的实用稳定24-33
    3.1 单时滞系统的实用稳定性24-28
    3.2 多时滞系统的实用稳定性28-33
第四章 含不确定项的的广义时滞系统的实用稳定33-39
    4.1问题描述33-34
    4.2主要结果34-39
参考文献39-41
个人简历41-42
致谢42
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