| Switched systems are important study objects in the modern control theory. In the actual switched systems, such systems are very complicated due to the interaction among time delays, uncertainties, interferences inside or outside of systems and switched mechanism. Therefore, researches on the stability for switched time-delay systems and the method to deal with uncertainties and interferences for switched systems are of great significances. This thesis studies minimax control methods and stable conditions for several kinds of switched systems based on the three basic problems. The main contributions are as follows.Firstly, for a class of linear time-delay switched systems with interference, the state feedback controller and the minimax controller are designed respectively. Moreover, the asymptotically stable sufficient condition, under any switching signals, of such systems is given. Also, the convex combination method is introduced to deal with the unstable switched subsystems. Basing on this method, the asymptotically stable sufficient condition is researched, and the state feedback controller and switching rules are designed.Secondly, the average dwell time method is introduced into the linear time-delay switched systems with interference and uncertainties. Based on the minimax method, the interference is processed, and the sufficient condition of robust exponential stability for switched systems with constant time-delay is given. Then, the results are extended to switched systems with time-varying delay. Moreover, the stability for linear time-delay switched systems including stable and unstable subsystems is considered. By getting activation time ratio between stable subsystems and unstable ones, sufficient conditions are given to ensure exponential stability of switched time-delay systems.Thirdly, the asymptotical stability problems are studied for a class of continuous switched systems whose state is incomplete measurable and a class of discrete switched systems, respectively. For the first class systems, based on the minimax method, the interference is processed. Then, considering two cases that all subsystems are stable and all subsystems are unstable, common Lyapunov function and multiple Lyapunov function methods are applied respectively. Sufficient conditions of asymptotical stability for switched systems under arbitrary switching signal and switching rules based on state observer are given, and at the same time, state feedback controller based on the output of observer is designed. Besides, the stability for discrete switched systems with interference is proposed, considering two cases that all subsystems are stable and all subsystems are unstable, sufficient conditions of asymptotical stability for switched systems under arbitrary switching signal and designed switching rules are given by transforming non-linear matrix inequalities into linear matrix inequalities.Finally, the results of the thesis are summarized and the thesis indicates some problems which deserve further study. |
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