Stability And Robust Control For Switched Systems With Time-varying Delay

A switched system is a dynamical system which consists of continuous time subsystems or discrete time subsystems and a rule adjusting the switching between them. Time-varying delay is common in control engineering, such as communication and the nuclear reactor. In recent years, many methods have been employed in the research of stability and the synthesis of the controller for switched systems. some results have published, which can reduce the conservative and improve the parameter stability. Combination of switched systems with time-varying delay is the switched systems with time-varying delay. In practical engineering, there are some unknown factors, so the study of uncertain switched systems with time-varying delay is more meaningful and valuable, at the same time, the study on this system is more challenging than the general ones.In this paper, we study the stability and robust control problems of switched systems with time-varying delay. Lyapunov stability principle is used in this paper. By using the method of Jensen integral inequality and reciprocal convex combination, we design a more general Lyapunov function to achieve the conditions for the exponential stability and robust stabilization, then we change these conditions into solvable linear matrix inequality, three questions about the stability are studied including: the stability for switched systems with time-varying stability; robust stabilization for uncertain switched systems with time-varying delay; robust H∞ control for linear switched systems with time-varying delay.Concretely, the research directions and significance of the switched system are given in the first chapter, about the main research results of this paper, in the second chapter, based on the average dwell time method, we analyze the condition of stability for the system under arbitrary switching. By using the reciprocal convex combination method and the Jensen integral inequality method, we obtain a smaller upper bound, as well as the linear matrix inequality which is a criterion for the stability of switched systems with time-varying delay. In the third chapter, using the Jensen integral inequality and reciprocal convex combination method, we get the sufficient conditions of stability and the existence of controller for the switched systems with time-varying delay, a robust H∞ controller design problem is discussed. In the fourth chapter, using multiple Lyapunov function method, we combine with Jensen integral inequality and reciprocal convex combination technique to study robust stabilization of uncertain switched systems with time-varying delay under a switched rule.At the end of the article, a summary of the research work is given.