基于改进型积分不等式的时滞系统稳定性分析

发布时间：2018-02-01 03:40

本文关键词： 分布式时滞系统中立型时滞系统 Lyapunov-Krasovskii泛函线性矩阵不等式　出处：《青岛大学》2017年硕士论文　论文类型：学位论文

【摘要】：实际系统中时滞因素的存在严重影响着系统的动态行为。多年来,对时滞系统稳定性的研究一直是系统理论领域的重要课题,也受到社会各界学者的广泛关注。本文应用李雅普诺夫稳定性理论,对两类时滞系统进行稳定性分析,得到了判定系统稳定的充分条件。本文主要的工作是:首先,应用自由权矩阵技术及矩阵不等式方法,得到一个改进型的二重积分不等式。与Wirtinger型二重积分不等式对比发现,在理论和实际应用中均能使系统的保守性降低。其次,分析分布式时滞系统和中立型时滞系统的稳定性。构造恰当的Lyapunov-Krasovskii函数并应用该改进型不等式,得到了新的判定这两类系统稳定的充分条件,并列举数值例子进行对比。仿真结果表明,本文得到的最大时滞上界值均大于以往文献的值,说明应用本文提出的不等式方法能有效地降低系统的保守性。本文的研究内容对提高系统稳定性分析方法具有重要意义。最后,对两类时滞系统的稳定性分析过程归纳、总结,针对已有的理论成果,提出了今后研究工作的规划和设想。
[Abstract]:The existence of time-delay factors in practical systems seriously affects the dynamic behavior of systems. For many years, the study of the stability of time-delay systems has been an important topic in the field of system theory. This paper applies Lyapunov stability theory to analyze the stability of two kinds of time-delay systems. The main work of this paper is as follows: firstly, the free matrix technique and matrix inequality method are used. A modified double integral inequality is obtained. Compared with the Wirtinger type double integral inequality, it is found that the conservatism of the system can be reduced both in theory and in practice. The stability of distributed time-delay systems and neutral time-delay systems is analyzed. The appropriate Lyapunov-Krasovskii function is constructed and the improved inequality is applied. A new sufficient condition for judging the stability of these two systems is obtained, and numerical examples are given to compare them. The simulation results show that the maximum delay upper bound values obtained in this paper are higher than those in previous literatures. It shows that the inequality method proposed in this paper can effectively reduce the conservatism of the system. The research content of this paper is of great significance to improve the stability analysis method of the system. Finally. The process of stability analysis for two classes of time-delay systems is summarized. According to the existing theoretical results, the planning and assumption of the future research work are put forward.
【学位授予单位】：青岛大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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