Analysis And Design Of Stability Of Positive Switched Systems

As a kind of hybrid systems, a switched system combines the discrete states and thecontinuous states. It consists of a family of dynamical subsystems and a rule, whichcoordinates switching role between these subsystems. In this paper, the involving rule, calledswitching signal, determines the switching manner between the subsystems. In the real world,many physical systems involve variables that have a nonnegative sign, for example,population of animals, absolute temperature and concentration of substances. Such a systeminvolves the positive system. That is to say, whenever their initial condition or the input isnonnegative, their state and output is still nonnegative. If we add the switching signal topositive systems for further research, we get the so called positive switched system that willbe studied in this paper. In the past ten years, positive switched systems have attracted moreand more interest because of their extensive application in the area such as economics,biology, communications, and so on. At the same time, it should be noted that the analysis ofthe stability of positive switched systems, compared with general switched systems, is achallenge. However, in order to obtain satisfactory results, we have to combine with positivesystem and the related characteristics of switched systems.This article focuses on the stability of switched systems and positive switched system(including linear and nonlinear cases) by using some methods developed for positive systems.Its contents are arranged as follows:In chapter one, we will introduce the background, history of development of switchedsystems and positive switched systems, and the main contents of this paper.In chapter two, the basic knowledge required in this paper is introduced.In chapter three, we first study delay-independent stability for a class of positiveswitched nonlinear systems with unbounded time-varying delays under arbitrary switching.Then, we extend the result to the case of time-varying system matrix. Finally, we studystability of positive switched nonlinear systems with mixed time-varying delays underarbitrary switching.In chapter four, we study the stabilization of positive switched linear and nonlinear systems by using the average dwell time method. Firstly, we study the exponential stability ofpositive switched linear systems with mixed time-varying delays. Then, the result is extendedto a class of switched systems with general forms. In the end, we study the global exponentialstabilization of a class of switched nonlinear systems with mixed time-varying delays.Summary and outlook are given in chapter five.