Dissipativity And Robustness Analysis Of Delayed Control Systems Based On LMI Technique

The theory of dissipativity has drawn many researchers' attention since it was introduced in 1970s by Jan.C.Willems and it has found applications in many areas such as stability theory,chaos and synchronization theory,system norm estimation,and robust control.Beside,time delay exists extensively in various practical control systems,such as aircraft,chemical engineering control systems,long transmission lines in pneumatic systems,and communication networks.Therefore,the study of dissipativity and robustness analysis for delayed control systems have become one of hot topics in the fields of international control engineering.This paper mainly deals with the dissipativity and robustness analysis of de-layed control systems.It mainly includes:In Chapter 1,the background of this article and some former results are intro-duced.Moreover,we provide the structure of the thesis.Finally,some important lemmas of this paper are given.In Chapter 2,by constructing a set of appropri-ated Lyapunov-Krasovskii functionals and employing integral inequality and free weighting matrix method,some delay-dependent dissipativity and robustness cri-teria of linear time-delay system are obtained in terms of linear matrix inequalities(LMIs).In addition,the design method of the state feedback controller for lin-ear time-delay systems is given.Finally,the effectiveness and superiority of the proposed results are evidenced by two illustrative numerical examples.In Chap-ter 3,by constructing a set of appropriated Lyapunov-Krasovskii functionals and employing Newton-Leibniz formulation and the method of convex combination,some dissipativity and robustness criteria that are dependent on the upper and lower bounds of the mixed interval delays for neural networks are derived in terms of LMIs.Finally,two numerical examples and their simulations are provided to demonstrate the effectiveness of the proposed criteria.