The Stabilization Of Positive Switched Linear Systems

For a positive system,if the initial state of the system is nonnegative,the system will remain nonnegative for the next time.Positive switched linear system(PSLS)is composed of multiple positive systems and a switching signal,so PSLS has the properties of both positive system and switched system.In other words,if the initial value of PSLS is nonnegative,then the state of the system will be nonnegative under arbitrary switching signal.At present,PSLS is widely used in many fields,such as aircraft control,network control,power electronics and so on.Therefore,researchers put forward a variety of methods to study the stabilization of PSLS.We will study the stabilization of PSLS from different perspectives.This paper is organized as follows:In Chapter 1,the generation and development of switched system,positive system and PSLS are introduced.In Chapter 2,the basic knowledge and symbols to pave the way for the following are defined.In Chapter 3,the stabilization of continuous-time time-invariant PSLS with impulse is studied firstly,then it is extended to continuous time-varying PSLS with impulse,and the stability of discrete-time PSLS is also considered.In Chapter 4,the stability of PSLS under state-dependent switching signal is studied by using Lyapunov-Metzler inequality,and the stability of PSLS with time delay is also considered.In Chapter 5,the stabilization of discrete-time PSLS is studied by using weakly switched linear copositive Lyapunov function,in which all subsystems are marginal stable.In Chapter 6,two different methods are used to study the stabilization of continuous-time PSLS with unstable subsystems.In Chapter 7,we summarize the important achievements of the whole paper,and look forward to the future research.