Research On Stability Of Switched Systems Based On Positive System Theory

As a kind of hybrid systems,a switched system combines the discrete states and the continuous states.It consists of a family of dynamical subsystems and a rule(or switching signal),which regulates the switching subsystems.In the real world,many physical systems involve variables that have a non-negative sign,such a system involves the positive system.In this paper,we consider the stability problem of a class of switched systems which can be studied by using the stability theory of positive system.In this paper,some new exponential stability results of switched systems are given in this paper.The contents are as follows:In Chapter I,this chapter briefly introduces the development status of the switching system,the positive system and the positive switching system,and introduces the main contents of this paper.In Chapter II,we briefly introduce the basic knowledge and notations that used in this paper.In Chapter III,first of all,this chapter introduces exponential stability of switched linear systems with time delay and nonlinear disturbance,we give the criterion of exponential stability of the system,then we study the exponential stability of switched nonlinear systems,and give the sufficient conditions of exponential stability.Finally,numerical examples are given to illustrate the feasibility of the results.In Chapter IV,this chapter investigates the exponential stability of switched linear systems and nonlinear systems by means of average dwell-time.We study exponential stability of switched systems with time delay and nonlinear disturbance;second,the switched nonlinear system with delays will be studied;Finally,numerical examples are given to illustrate the feasibility of the results.In Chapter V,we give the summary and prospect of the research.The main work and innovation points of this paper are briefly summarized.Some future research about this paper is also presented.