基于正系统理论的切换系统稳定性研究

发布时间：2018-04-21 10:14

本文选题：切换系统 + 正系统　；参考：《济南大学》2017年硕士论文

【摘要】：切换系统作为混合动力系统的一种,它集合了离散状态和连续状态,也就是由一系列子系统以及在这些子系统之间起协调切换作用的规则(或者说切换信号)所组成的混合动力系统。另外,在现实世界中,许多物理系统所涉及到的变量都是非负的,这样的系统就要涉及到正系统。本文考虑了几类可以借助于正系统稳定性理论方法进行研究的切换系统的稳定性问题。由于结合了正系统和切换系统的相关特性,本文给出了切换系统若干新的指数稳定性结果。其内容安排如下:第一章,简要介绍了切换系统、正系统和正切换系统的发展现状,并介绍本文所要研究的主要内容。第二章,简要介绍本文需要用到的基本知识以及符号定义。第三章,首先介绍具有时滞和非线性扰动的切换线性系统的指数稳定,给出了系统指数稳定的判据,其次研究了切换非线性系统的指数稳定性,进而给出了系统指数稳定的充分条件,最后数值举例并仿真作图说明了结果的有效性。第四章,运用平均滞留时间的方法,研究切换线性系统和切换非线性系统的指数稳定性。首先,研究了带时滞和非线性扰动的切换线性系统的指数稳定性,其次研究了带时滞的切换非线性系统的指数稳定性,最后数值举例并仿真作图说明了结果的有效性。第五章,对研究的内容总结和展望。简要归纳本文内容,总结创新之处,并给出了对本文今后研究的想法和展望。
[Abstract]:As a kind of hybrid power system, switched systems are composed of discrete state and continuous state. In other words, a hybrid power system is composed of a series of subsystems and the rules (or switching signals) that coordinate the switching between these subsystems. In addition, in the real world, the variables involved in many physical systems are nonnegative, and such systems involve positive systems. In this paper, we consider some stability problems of switched systems which can be studied by means of positive system stability theory. In this paper, some new exponential stability results of switched systems are given because of the correlation between positive systems and switched systems. The contents are arranged as follows: in Chapter 1, the development of switched system, forward system and forward switched system are introduced briefly, and the main contents of this paper are introduced. The second chapter briefly introduces the basic knowledge and symbol definition of this paper. In chapter 3, the exponential stability of switched linear systems with time delay and nonlinear perturbation is introduced, and the criteria for exponential stability of switched linear systems are given. Secondly, the exponential stability of switched nonlinear systems is studied. Furthermore, sufficient conditions for exponential stability of the system are given. Finally, numerical examples and simulation diagrams are given to illustrate the validity of the results. In chapter 4, the exponential stability of switched linear systems and switched nonlinear systems is studied by using the method of mean residence time. Firstly, the exponential stability of switched linear systems with time delay and nonlinear perturbation is studied. Secondly, the exponential stability of switched nonlinear systems with time delay is studied. Finally, numerical examples are given to illustrate the effectiveness of the results. Chapter five summarizes and prospects the content of the research. This paper briefly summarizes the content of this paper, summarizes the innovation, and gives the ideas and prospects for the future research of this paper.
【学位授予单位】：济南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O19

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