基于平均暂留时间的切换随机系统稳定性研究

发布时间：2018-08-12 11:37

【摘要】：切换系统作为混杂动态系统的一个重要组成部分,它由子系统与切换规则共同构成。切换系统按照一定的切换规则来确定当前运行的子系统。近年来,切换系统被广泛应用于大型供电网络、机器人产业、交通运输、复杂化学过程等众多领域。对于切换系统而言,寻找有效的切换规则,使得切换系统在某一切换规则下保持状态稳定,这一直是切换系统研究中的一个重点问题。本文将基于平均暂留时间的概念,考虑了切换系统中不同子系统的自身特性对切换系统的稳定性影响。在模态依赖的假定条件下,研究了切换随机系统的p阶矩稳定性与输入状态稳定。同时,在本文中还将考虑当切换系统中具有部分不稳定子系统时,这些不稳定的子系统对切换系统稳定性的影响。全文的主要内容总结如下:第一章是绪论,阐述了本文的研究背景以及意义;介绍了当前国内外相关的研究成果;最后对全文的内容和结构进行了梳理。第二章,当切换随机系统的子系统都稳定时,使用模态依赖的平均暂留时间的概念,研究了切换随机系统的输入状态稳定性,并给出了切换随机系统的状态估计,在这种状态估计的基础上得到了切换随机系统输入状态稳定的充分条件。第三章,当切换随机系统的子系统是部分稳定时,在模态依赖假设下,Lyapunov函数算子的时变上界、子系统的运行时间和平均暂留时间都是模态依赖的,切换随机系统的状态估计是利用一些辅助的方程和Lyapunov-Razumikhin方法导出来的。通过使用模态依赖下的平均暂留时间的概念,研究了关于切换随机时滞系统的p阶矩稳定和p阶矩渐进稳定以及p阶矩指数稳定。另外,对于具有部分稳定子系统的切换随机时滞系统,通过使用模态依赖下的平均暂留时间的方法,结合模态依赖下的Lyapunov函数算子的时变上界,在给定的系统状态估计下,给出了输入状态稳定和积分输入状态稳定的充分条件。第四章总结全文的研究成果,并给出了本文的研究不足之处,以及展望未来的研究计划。
[Abstract]:As an important part of hybrid dynamic systems, switched systems consist of subsystems and switching rules. The switching system determines the current operating subsystem according to certain switching rules. In recent years, switching systems have been widely used in large power supply networks, robot industry, transportation, complex chemical processes and many other fields. For switched systems, it is an important problem in the research of switched systems to find effective switching rules to keep the state of the switched systems stable under a certain handover rule. In this paper, based on the concept of average temporary time, the influence of the characteristics of different subsystems on the stability of switched systems is considered. Under the assumption of modal dependence, the p-order moment stability and input state stability of switched stochastic systems are studied. At the same time, the effect of these unstable subsystems on the stability of switched systems will be considered when there are some unstable subsystems in switched systems. The main contents of this paper are summarized as follows: the first chapter is the introduction, which describes the background and significance of this paper; introduces the current domestic and foreign related research results; finally, the content and structure of the full text are combed. In chapter 2, when the subsystems of switched stochastic systems are stable, the input state stability of switched stochastic systems is studied by using the concept of modal dependent mean transient time, and the state estimation of switched stochastic systems is given. Based on the state estimation, a sufficient condition for the input state stability of switched stochastic systems is obtained. In chapter 3, when the subsystem of switched stochastic system is partially stable, the time-varying upper bound of Lyapunov function operator is assumed to be modal dependent. The state estimation of switched stochastic systems is derived by some auxiliary equations and Lyapunov-Razumikhin method. By using the concept of average transient time under modal dependence, the p-order moment stability, p-moment asymptotic stability and p-moment exponential stability of switched stochastic time-delay systems are studied. In addition, for switched stochastic time-delay systems with partially stable subsystems, by using the method of average transient time under modal dependence and the time-varying upper bound of Lyapunov function operator under modal dependence, the given system state estimation is given. Sufficient conditions for input state stability and integral input state stability are given. The fourth chapter summarizes the research results of this paper, and gives the shortcomings of this study, as well as the future research plan.
【学位授予单位】：安徽工程大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP13

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