一类混杂系统—切换系统的定性，稳定性分析

【作者】 高凤银；

【导师】 钟守铭；

【作者基本信息】 电子科技大学 ， 应用数学， 2008， 硕士

【摘要】 切换系统是一类离散和连续的动态系统相组合的混杂系统。它可以看作是由几个微分方程及作用在其中的切换规则构成。近十年来,许多人对这类系统关注并深入研究,取得了很多结果。这些结果大都集中在稳定性方面。本文系统地研究了时滞切换系统的稳定性,主要探讨了离散时滞和分布时滞的连续和离散切换系统的稳定性问题。将已有的成果给予了完善。本文主要分为以下四个方面的内容:1.研究了一类带离散和分布时滞的线性切换系统的一致渐近稳定性,通过构造Lyapunov泛函,利用Riccati方程方法,给出在时滞充分小的条件下系统稳定性的充分条件。在结论之后,给出例子说明了系统的可行性。2.进一步研究了带离散和分布时滞的线性切换系统的指数稳定性和L₂增益性能。应用线性矩阵方法给出了带离散和分布时滞的线性切换系统的指数稳定的与时滞有关的充分条件,并讨论了系统的L₂-增益性能。3.研究了一类带时滞的离散切换控制系统平凡解的渐近稳定性的新标准,主要运用第二Laypunov方法,条件是以线性不等式的形式给出,结果是与时滞无关的。4.进一步研究了一类带时滞的不确定离散切换控制系统平凡解的渐近稳定性的新标准,通过构造Laypunov泛函,运用线性不等式方法得到系统渐近稳定的结果,并通过几个例子验证结果的可行性。更多还原

【Abstract】 Hybrid system is a combination of discrete and continuous dynamical systems. These systems arise as models for phenomena, which cannot be described by exclusively continuous, or exclusively discrete processes. There are many perfect results on the stability of switching systems.This paper deals with the problem of stabilization of switched systems with time delays, and focuses on the stabilization of switched systems with discrete time delay and distributed time delay. It makes the existing results more perfect.The paper is organized as follows:1. This paper deals with the problem of a type of linear switching systems with discrete and continuous time delay. By constructing Lyapunov functional under a condition on the time delay, we show it stabilizes the system for sufficiently small delays.2. In this paper, we study stability and L₂ -gain for a class of switched systems with discrete time delays and distributed time delays. Sufficient conditions for exponential stability and weighted L₂ -gain are developed. These conditions are delay-dependent and are shown in the form of linear matrix inequalities. The state decay estimate is given. Several examples illustrate the effectiveness of the proposed method.3. In this paper, we obtain some criteria for determining the asymptotic stability of the zero solution for some classes of delay-difference system-discrete time switched systems, and delay-independent robust stability and stabilization of it. We mainly used a discrete version of the second Lyapunov method.4. This article gives a novel criterion for the asymptotic stabilization of the zero solutions of a class of switched systems with delays in control input. By constructing Lyapunov functional, we obtained the criterion which is expressed in terms of matrix inequalities. The results are more advanced than the references. Numerical examples are presented to illustrate the effectiveness of the theoretical results.更多还原