Stability Analysis And Synthesis Of Linear Systems With Time-Varying Delays

Time-delay is a common phenomenon in engineering systems. Time delay can be a source of instability and poor performance. Thus, the stability of time delay systems have been widely considered by more and more researchers. With the development of industrial technology, only analyze the systems can not meet the actural requirments. We hope systems can obtain some special performance by the design of controller. Such as Asymptotic stability, H∞output tracking performance. Base on the requrment, considerable attention has been paid to the analysis and synthesis of controllers for time delay systems.This paper studies the controller design for linear systems with time-varying delay. Based on the Lyapunov second method, using linear matrix inequalities (LMI) technology, we will study the methods of controller-designing such as the controller design for H-Infinite output tracking control for neutral systems with time-varying delay, robust H-Infinite filtering for uncertain discrete-time systems with time-varying delay and the analysis of stability for linear switched systems with time-varying delay.Our first chapter of this paper is a brief introduction about purposes, the significance and the current research results of the linear systems with time-varying delay, as well as the main work of this paper. In the second chapter, some of the basic concepts and basic theory will be introduced. In the third chapter, the problem of controller design for H-Infinite output tracking control for neutral systems with time-varying delay is investigated. A method of designing contoller can be obtained by Lyapunov theory and H-Infinite output tracking performance can be satisfied. In the forth chapter, the problem of robust H-Infinite filtering for uncertain discrete-time systems with time-varying delay is investigated. By using the same method of chapter three, the result deduces a new sufficient condition for systems with polytopic-type uncertainties. Based on the result above, the H-Infinite filter is designed in terms of linear matrix inequalities (LMIS). In the fifth chapter, we consider the problem of stability for linear switched systems with time-varying delay, Based on a new integrate inequality with less conservativeness result, and a new sufficient condition on stability of systems is derived. Finally, numerical examples are appear in each chapter in order to indicate that the results presented in this paper are effective and less conservative and directions for future are given.