Study On The Asynchronous Control Problem For Classes Of Switched Systems

As an important class of hybrid systems,switched systems can describe many practical and complex systems.Switched system is composed of a limited number of subsystems and a switching signal.The switching signal controls the switching of these subsystems.Due to their extensive application in the fields of communication,chemical industry,electric power,manufacturing and so on,many results have been reported in recent years about stability,stabilization,observation,filtering and reduced order.However,it is noticeable that most of the results about switched systems have been obtained under the assumption that the mode of controller is always synchronous with the mode of subsystem,which is difficult to implement in the actual system.The situation that the mode of controller is different from the mode of subsystem is called asynchronous switching phenomenon.The operational mechanism and dynamical behaviors of switched systems will become much more complex with the asynchronous switching phenomenon.Therefore,study on the asynchronous control problem of switched systems is significative and challenging.This dissertation concerns the asynchronous control problems of switched systems,the main contributions are as follows:Chapter 2 concerns the issue of robust asynchronous control of time-varying delay switched systems.Based on Lyapunov-Krasovskii functional and free weight matrix approach,considering actuator saturation,sufficient conditions for exponential stability of the closed-loop systems are proposed.Then the problems of solving anti-windup compensation gain matrices and expanding the domain of attraction are converted into an optimization problem.Considering stochastic disturbance,sufficient conditions for finite-time L2-L?boundedness of the closed-loop systems are proposed.The Lyapunov-Krasovskii functional is improved to release the constraint that derivative of time-varying delay should be less than one,which reduces the conservativeness.Chapter 3 studies the sampled-data asynchronous control of the switched fuzzy systems.Considering the asynchronous switching phenomenon cased by the sampling of subsystem mode,based on the input delay approach and T-S fuzzy control approach,sampled-data nonlinear switched systems can be converted into time-varying delay switched T-S fuzzy systems with asynchronous switching.Sufficient conditions for exponential stability of the closed-loop systems are proposed.By applying the mode-dependent average dwell time approach,the conservativeness is reduced.Chapter 4 investigates the distributed event-triggered sliding mode control of switched systems.Considering distributed sampling and communication,the frame of distributed event-triggered sliding mode control of switched systems with uncertainty and unmeasurable states is proposed.The corresponding event trigger condition,observer and sliding mode control law are designed.Based on Lyapunov-Krasovskii functional and mode-dependent average dwell time approach,sufficient conditions for H? exponential stability of the closed-loop systems are proposed.Chapter 5 addresses sliding mode control of switched positive systems with asynchronous switching.Considering the positivity and unmeasurable states,the positivity,exponential stability and L1-gain performance are analyzed through the mode-dependent appropriate co-positive type Lyapunov-Krasovskii functional and mode-dependent average dwell time approach.An iterative algorithm is designed to solve the observer and controller,which reduces the condition in the parameter selection method that the rank of controller coefficient matrix is confined to one.Chapter 6 concerns the asynchronous control problem of Markov switched systems.Considering singular Markov switched systems with asynchronous switching,by modeling the switching delay and state delay as Markov chains,the closed-loop systems can be expanded as delay-free Markov switched systems.Necessary and sufficient conditions for admissibility of the closed-loop systems are proposed and are rewritten as matrix inequalities.Considering the asynchronous switching phenomenon caused by modal identification failure,the stability and stabilization of continuous-time Markov switched systems and discrete-time Markov switched systems are analyzed.Finally,the results of the dissertation are summarized and further research topics are pointed out.