Robust Stability Of Switched Systems With Time-delay

Switched system is an important class of Hybrid Dynamic System. Switched system with time-delay is a type of systems with switching and time-delay. Its behavior character is very complex because of the interaction among the continuous dynamic, discrete dynamic and time-delay. The problems of the state feedback robust stability for three different types of linear switched systems with time-delay are studied in this dissertation. These three problems can be solved by means of common Lyapunov function, multiple Lyapunov function, linear matrix inequalities, completeness condition and so on. All summarize as follows:First, the problem of robust controllers of a class of switched system with time-delay and exterior disturbance is considered. A kind of robust state-feedback controller is constructed by using completeness condition and common Lyapunov function method, the switching strategy is also designed. With the given switching laws, the controllers guarantee that the states of closed-loop systems asymptotically converge to equilibrium point. In this chapter, the exterior disturbance is different from the ordinarily disturbance, and it's another kind of very important disturbance. For every subsystem, it does not satisfy matching conditions, but for the whole switched systems, it's similar to the matching conditions. The results are available for the switched systems with time-delay which have several subsystems. The results are proved to be valid by using of digital simulation at last.Second, we discuss the robust stabilization problem of a class of uncertain switched system with time-delay and uncertainty. This type of switched systems not only has uncertainty in structure and in input channel, but also has exterior disturbance which does not satisfy so-called matching condition. By using the completeness condition, multiple Lyapunov function method and common Lyapunov function method, the state feedback robust controllers of switched systems and switching strategy are designed on condition that each subsystem needn't to meet with the requirement of stabilization. The sufficient condition of robust stabilization for switched systems with time-delay is obtained. The results are proved to be valid by simulation at last.Last, we discuss the robust stabilization problem of a class of switched linear system with time-varying delay and uncertainty. A kind of robust state-feedback controller is constructed by using completeness condition and common Lyapunov function, the switching strategy is also designed. With the given switching laws, the controllers guarantee that the states of closed-loop systems asymptotically converge to equilibrium point. The results are proved to be valid by simulation at last.The summary and the problems which can be more investigated are given at theend of the thesis.