Finite Time Stability Analysis And Robust Controller Design For Switched Systems

Switched system is generally considered to be a typical hybrid dynamic system,which consist of a class of subsystems and switching signals related to the control subsystem switching rules.Switched systems can be used to describe many practical systems with a wide range of applications,such as motor systems,network control systems,robotic control systems,and water quality systems.An important feature of the switched system is that when all subsystems are stable,the designed switching signal does not necessarily guarantee the stability of the switched system.Under the action of different switching signals,the dynamic performance of the switching system is complex and diverse.The essence of a switched system is not a simple superposition of the nature of each subsystem,it may even have different properties.On the other hand,the research on the switching system mainly focuses on the Lyapunov stability,that is,the stability in the infinite interval is studied.However,in practical engineering process,in order to meet the engineering needs,more attentions is paid to the transient performance of the system in a limited interval For the finite-time stability problem,Dorato proposed the concept of finite time stability in 1961.Subsequently,Weiss proposed the concept of finite-time boundedness in 1967 and obtained extensive research in academia.Sliding mode control is an effective robust control scheme for the effects of uncertain parameters and disturbances in the processing system.The method has the advantages of fast response,simple construction process,and insensitivity to uncertain parameters and external disturbances.In recent years,there have been more and more researches on asynchronous switching and sliding mode control of switching systems,but there are few literatures on the transient control problem of switched systems in finite time interval.Through the techniques of Lyapunov function,average dwell time method and linear matrix inequalities,the finite-time control problem of the switched system is systematically analyzed and studied in this paper.The specific research contents are as follows:(1)For a class of Lipschitz nonlinear time-delay switched systems,a suitable state feedback controller and switching signal are designed,so that the closed-loop switching system is finite-time bounded and meets the given L? performance index.(2)For a class of Lipschitz nonlinear time-delay switched systems,the finite-time H? asynchronous control problem is studied.By designing a suitable elastic asynchronous controller,the corresponding closed-loop switching system is finite-time bounded and satisfies a prescribed H? performance.(3)The observer-based finite-time sliding mode control problem for a class of uncertain switched systems with time-delay is studied.According to the system model,a general sliding surface associated with the estimated state is constructed.Based on the sliding mode control theory,a suitable sliding mode controller is designed to enable the system state to be driven to the designed sliding surface.By selecting the appropriate Lyapunov function and using the average dwell time method and partition strategy lemma,sufficient conditions are given for the system state to be finite-time bounded at the sliding mode approach stage and the sliding mode dynamic stage.