Exponential Stability And Boundedness Of Switched Delay Systems With Nonlinear Disturbances

Switched system is an important model for studying hybrid system theory in the perspective of controlling science.It is an international forward direction of hybrid system theory research,which is mainly used for the description,analysis and control of complex large systems.In general,a switched system consists of a series of subsystems and a switching signal which indicates the relation between subsystems.Each subsystem is usually described by a definite differential equation or difference equation,and only one subsystem is active at some time instant.When the system switched,the state trajectory of the system will remain unchanged or jump.In this paper we study a class of switched time-varying systems with time-varying delay and nonlinear disturbance.Based on common Lyapunov function and a generalized integral inequality with time-varying delay,new sufficient conditions for exponential stability and boundedness of the system are established when the involved nonlinear disturbance satisfies linear and nonlinear growth conditions,respectively.Finally,we extended the results to the switched delay system with both distributed delay and nonlinear disturbance.In Chapter I,we mainly introduce the development process and the research statu s of switching system stability,and briefly introduce the application of integral inequal ity in the field of system stability theory.In the meantime,the main content of this p aper is presented.In Chapter II,we mainly deal with the preparation work,including the definition of symbols involved in the paper,the basic concept,and the necessary lemma in the process of proof.In Chapter III,we study a class of switched time-varying systems with time-varying delay and nonlinear disturbance.Based on common Lyapunov function and a generalized Gronwall-Bellman integral inequality with time-varying delay,the sufficient conditions for exponential stability and boundedness of the switched system under three nonlinear disturbances are given,respectively.Next,in order to reduce the conservatism of the above method,we improve the method,namely the system is deformed before constructing the common Lyapunov function,and give a more general sufficient condition.This increases therange of application of the results to a certain extent.Finally,numerical examples are given to illustrate the effectiveness.In Chapter V,we study a class of switched time-varying systems,which contains both nonlinear disturbances and distributed delay.By constructing a common Lyapunov function,we give the sufficient conditions for the exponential stability and boundedness of the system with three kinds of nonlinear disturbances.Finally,numerical examples are given to illustrate the feasibility of the results.