Stabilization Of Switched Linear Systems With All Subsystems Unstable And Its Applications

Switched system is a special kind of hybrid systesms,which consists of a series of subsystems and a switching signal that determines how to switch between subsystems.When all subsystems are positive systems,we call the switched system a switched positive system.The switched(positive)system has a wide range of applications,including multi-agent consensus,aircraft control,and gasoline engine control.Moreover,two-dimensional(2-D)system occupies a major role in image data processing,network system stability,and multivariable control applications.In this thesis,we aim to further study the basic theory,modeling methods and practical applications of switched(positive)system,time-varying switched system and 2-D time-varying switched system.This thesis is organized as follows:In Chapter 1,the generation and development of switched system,time-varying switched system and 2-D time-varying switched system are presented.The main purpose,the basic knowledge and symbols of this thesis are also introduced.In Chapter 2,employing the switched linear time-varying copositive Lyapunov function method and the analytical techniques developed in positive system,the(practical)exponential stability of continuous-time positive switched linear system with impulses and unstable subsystems under mode-dependent range dwell time switching is investigated.The main results are also applied to the(practical)consensus problem of multi-agent systems with switching topologies.In Chapter 3,the stability of positive switched linear system with all subsystems unstable is studied through the hybrid minimum switching method.A time-varying state feedback controller is also designed.Moreover,the main results are applied to the treatment problem of genetic regulation systems.In Chapter 4,the exponential stability of discrete-time positive switched linear system with all subsystems unstab le under restricted switching is analyzed by using the switching path method which is based on switching directed graphs and state component directed graphs.In Chapter 5,utilizing the switching linear time-varying copositive Lyapunov function method,the exponential stability of continuous-time time-varying switched linear system with all subsystems unsta ble under mode-dependent range dwell time switching is explored.In addition,the main results are applied to the consensus of multi-agent system with switching topologies.In Chapter 6,the stability of a discrete-time 2-D time-varying switched linear system in which all subsystems are unstable is studied with the aid of time-varying scalar functions.In Chapter 7,the key results of the thesis are summarized and future research is discussed.