Stability Analysis And Controller Design For Interval Time-delay Systems Based On Improved Lyapunov Functional

It is well known that time-delay frequently occurs in many practical systems, such as telecommunications systems, chemical processes, manufacturing systems, electrical systems, economic systems and biological systems. It has been widely recognized that this is a major cause of poor performance and instability.Therefore, time-delay system has been an active research area in the past few decades. This article investigates the problem of delay-dependent stability analysis and robust performance analysis for linear system with interval time-varying delays.Firstly, by introducing some new Lyapunov functionals and using the reciprocally convex combination method to estimate the derivative of the Lyapunov functionals, some less conservative delay-dependent stability criteria for continuous delay systems with interval time-varying delay are obtained.Secondly, based on the proposed delay-dependent stability criteria, H￥ performance is obtained and H￥ state feedback controller is designed for a class of continuous time-delay systems with interval time-varying delay.Thirdly, by introducing some new Lyapunov functionals and using the reciprocally convex combination method to estimate the forward difference of the Lyapunov functionals, some less conservative delay-dependent stability criteria are obtained for discrete delay systems with interval time-varying delay.Finally, based on the proposed delay-dependent stability criteria, H￥ performance is obtained and H￥ state feedback controller is designed for a class of discrete time-delay systems with interval time-varying delay.