Minmax Robust Control For Uncertain Linear Switched Systems

With the development of science and technology, switched systems as a kind of important hybrid mixed dynamic system, has received more and more attention. The environment disturbance existing in actual engineering systems and the system uncertainties can destrioy the stability and performance of the system. During the recent years, we have made many achievements about robust control in uncertain linear switched system, however, only consider the disturbance existence without the discussion on effectiveness. The minimax robust control deals with the stability and performance of the control systems under the worst condition in disturbance and uncertainties, and makes the performance index least. Therefore, the study of minimax robust control for uncertain linear switched system has very important significance.Based on current research achievements of switched systems, combined minimax control theories, we considered the related issues of minimax control for uncertain linear switched system by means of the linear matrix inequalities and Lyapunov function methods. The main contents in this thesis are as follows:Firstly, we introduce the background of the switched system, receive the development situation of optimal minimax control, and sum up the significance of minimax robust control for uncertain linear switched system. Then we introduce the basic knowledge which including switched system’s model and characteristics, Lyapunov stability theory, linear matrix inequality (LMI). Meanwhile, some inequalities and lemmas are presented.Secondly, we discuss the minimax robust control for uncertain continuous switched system and uncertain discrete switched system respectively. First a sufficient condition for the existence of state feedback and dynamic output feedback optimal minimax controllers are obtained by using Lyapunov methods, the construction of local criterion fuction and linear matrix inequalities. Next, by means of the LMI, the design of optimal minimax controllers is transformed into the feasible prolem of a cetain LMI system. Finally, a numerical example is given to show the feasibility of the results.Finally, concluding remarks are presented, and some problems are also pointed out, which deserve further study.