Stability And Robust Stabilization Of Switched Systems With Time-delay

Switched systems with time-delay is a type of system with switching and time-delay, so its behavior character is very complex. Whether depending on time delays of the systems, the stability of switched systems with time-delay can be divided to delay-independent stability and delay-dependent stability.In this dissertation, we study delay-independent stability, delay-dependent stability and state feedback robust stabilization of linear switched systems with time-delay. These three problems can be solved by means of common Lyapunov function method, multiple Lyapunov function method, average dwell time method, linear matrix inequalities method, completeness condition and so on. All summarize as follows:Firstly, the problem of delay-independent stability of linear switched systems with time-delay is studied. By using multiple Lyapunov function method, two sufficient conditions of the delay-independent stability and two design methods of the switching law are obtained. The results can adapt for the switched systems with time-delay which have several subsystems. One of the results is proved to be valid by using of digital simulation at last.Secondly, in order to get less conservative and more general stability conclusion, the delay-dependent stability of linear switched systems with time-invariant delays is researched by using of multiple Lyapunov function method. The sufficient condition of the delay-dependent stability and the design method of the switching law are obtained. Then the stability of a class of switched systems with time-varying delays is studied by using of common Lyapunov function method. The sufficient condition of the delay-dependent stability and the design method of the switching law are obtained. All sufficient conditions obtained can be solved by linear matrix inequalities method. One of the results is proved to be valid by simulation at last.Lastly, we discuss the robust stabilization problem of two types of uncertain switched system with time-delay. Firstly by using the completeness condition and common Lyapuov function method, we study the robust stabilization problem of a type of uncertain switched systems with time-delay. This type of switched systems not only has uncertainty in structure and in input channel, but also has outside disturbance which does not satisfy so-called matching condition. The state feedback robust controllers without memory of switched systems and corresponding switching strategy are designed on condition that each subsystem needn't to meet with the requirement of stabilization. And the sufficient condition of robust stabilization for switched systems with time-delay is obtained. Then by using the method of average dwell time, we research the robust stabilization problem of another type of uncertain switched systems with time-delay. This type of switched systems not only has uncertainty in system matrices and in delay time matrices, but also has outside disturbance which satisfies so-called matching condition. We design the state feedback robust controllers without memory of uncertain switched systems with time-delay to guarantee the systems can be stabilized by any switching strategy on condition that the systems satisfy a given dwell time. The results are proved to be valid by simulation at last.