Finite-time Stability Of Switched Linear Systems And Its Application

Switched system is a hybrid system which is composed of a family of systems or subsystems and the switching rules which can coordinate them.In recent years,switched system theory has been applied to engineering practice and control theory.In many practical systems,their initial states are always nonnegative,so they are called positive systems.A positive system is a system in which nonnegative initial conditions lead to nonnegative state trajectories.Positive switched linear system is a complex positive system,which contains multiple positive subsystems,and each positive subsystem has a switching rule(i.e.switching signal).This kind of system has the characteristics of both positive system and switched system,and has a wide range of applications in biology,medicine,network communication,etc.On the other hand,in the research of switched linear systems,most of them are concerned with whether the system is asymptotically stable or not.However,in practical applications,there is no absolute ideal state of the system,and the system is often affected by various factors.In recent years,more and more researchers are devoted to the study of finite time stability.In this paper,the finite time stability of switched linear systems and positively switched linear systems is studied by constructing a new Lyapunov function.This paper is organized as followsIn Chapter 1,the generation and development of switched systems,positive systems and positive switched time-delay systems are briefly introduced,and the main purpose of studying switched time-delay systems is introduced.In Chapter 2,This paper briefly introduces the basic knowledge and symbol definition needed in this paper,which paves the way for the following.In Chapter 3,the FTS of general switched linear time-delay systems with arbitrary switching is studied by constructing time-varying quadratic Lyapunov function.At the same time,the FTS of positive switched linear time-delay systems is considered by using two different methods.In Chapter 4,we first construct a linear copositive Lyapunov function and design a suitable switching signal to make the general switched linear time-delay system reach FTS.Then we prove the FTS of the switched linear time-delay system under the mean residence time switching by two different methods.Then we apply the comparison principle to the application of the switched linear time-varying time-delay system in FTS.In addition,the FTS criteria for positive switched linear time-delay systems with impulses are considered.In Chapter 5,The research content of this paper is summarized and prospected.This paper briefly summarizes the important research results,summarizes the innovation and shortcomings,and looks forward to the future research direction of this paper.