H_∞Control For Switched Systems With Uncertain Time-delay

With the development of science and technology, the switched systems as important hybrid systems have received more and more concerns from domestic and foreign control sector. In practical engineering systems, some of the characteristics of the system and lack of understanding of the system lead to uncertainty and time-delay widespread, and thus undermine the stability of the systems. In recent years, some researches on the uncertain time-delay switched systems have success, but the research on the uncertain multiple-delays switched systems and the design of non-fragile state feedback control of uncertain time-delay switched systems is rare. Uncertain multi-time delay phenomenon and the fragile often appear, so it has great significance to study the two problems.Based on current research achievements of switched systems, stability theory of Lyapunov function and linear matrix inequalities, combined with control theory, we consider H∞control for uncertain multi-time delay switched systems and non-fragile state feedback H∞control of uncertain switched systems with time-delay in the particular switch signal and arbitrary signals. The main content are as follows:Firstly, we introduce the research background and status of switched systems, expound the developing situation of the control theory, show the great significance of researching H∞control of the uncertain time-delay switched systems. And in the paper, we introduce some basic concepts, the stability theory of Lyapunov function and some basic contents of linear matrix inequality, as well as some lemmas used in researching.Secondly, we discuss the H∞control of uncertain multi-time delay switched systems, give the sufficient conditions of H∞control of the uncertain multi-time delay switched systems. And we give the sufficient conditions of exciting H∞state feedback controller in non-autonomous systems. Thus a numerical example is given to show the feasibility of the results.Thirdly, we study the non-fragile state feedback H∞control problem of uncertain time-delay switched systems. In the uncertain time-delay switched systems, according to the fragile in solving the robust problem, we give respectively the sufficient conditions of exciting non-fragile state feedback H∞controller in particular switching signal and arbitrary switching signal. And then the numerical example is given to verify its validity.Finally, concluding remarks are presented, and some problems which deserve further study of the uncertain time-delay switched systems are also pointed out.