Stability Analysis Of Switched Systems

Switching system is a type of hybrid dynamical systems, which contains a family ofcontinuous-time or discrete-time subsystems, and a switching signal control theswitching between the various subsystems. Switched system is a special kind of hybridsystems which is studied from the perspective of systems and control theory. With thegreat development of hybrid systems, switching systems has been widely investigatedbecause of its relatively simple structure, ease of understanding, analysis and application.In real world, many of the natural, social and engineering systems will exhibit a differentmodel depending on various environments, such as power systems, traffic control,automotive, and so on. So these systems can be well modeled as switching system. Thestability theory is the foundation for the research of switched systems, so the first thing isto establish its stability theory in order to make a further discussion of the switchingsystem.In this paper, we consider the stability of switched systems. The paper is dividedinto five chapters and organized as follows:In chapter1, we introduce the history and development of theories of switchedsystems, involving basic definitions of switched system, the method of studyingswitched systems. At the end of this chapter, we give the brief statement of the mainwork.In chapter2, we divided into three sections. Applying Lyapunov functions, westudy the uniform stability, uniform asymptotic stability and uniform exponentialstability of discrete-time switched nonlinear systems. Some sufficient conditions areestablished for these stabilities.There are three sections in chapter3. In section3.1, we get some sufficientconditions of the exponential stability for uncertain switched systems with mixed timedelays by Lyapunov-Krasovkii functional approach and linear matrix inequalities. Insection3.2, we study the switched impulsive systems with mixed time delays, andapplying some impulsive delay differential inequalities, we obtain the sufficientcondition for exponential stability. There are four sections in chapter4. In section4.2, we investigate the exponentialstability of discrete-time switched systems, some criteria for exponential stability of thesystem are established based on linear matrix inequality and average dwell time method;using the same methods, in section4.3, we consider the uncertain discrete-time linearswitched systems with time-varying delays, and establish the sufficient condition ofexponential stability for the system.In chapter5, we conclude the main work in this paper and discuss future researchfor the stability of switched systems.