Sliding Mode Control Of Switched Systems With Time-varying Delay

Linear switched systems provide a framework to combine the linear systems with the complex or uncertain systems. So, they can have the advantages of both. Many intelligent control methods using the controller switching strategy to overcome the shortcomings of traditional single controller, and improve the system performance. In recent years, time-varying delay systems received attention continuously, the reason is that many practical systems inevitably contain time-varying delay. The time-varying delay can not be ignored, and may lead to system oscillation, divergence and even instability. Due to consider the delay will make the problem becomes very complex, the research results of switched systems with time-varying delay is rare. Since 1950 s, sliding mode control appears, it has become an e?ective robust strategy for incompletely modelled or nonlinear systems. In di?erent kinds of control systems, because of the sliding mode control has advantages of easy realization, fast response, good transient response, insensitivity to parameters uncertainties and external disturbances, so the sliding mode control is often used. The properties of sliding surface is pre designed, such as stability, disturbance rejection capability, tracking capability. It is worth noting, sliding mode control of switched systems with time-varying delay has few results been reported. The research in this aspect is very important, and challenging, and the conclusion of the study is very useful for researchers and designers in the field, this is the research purpose.This paper mainly studies the continuous time and the discrete time sliding mode control of switched systems with time-varying delay. In order to make the control system model is more accurate, the control performance to meet higher requirements, give full play to the sliding mode variable structure control with robust performance. In addition, because of the discrete system is often obtained by the continuous control method after discretization, there are many problems in the application of sliding mode control,this paper will directly analysis on the discrete system. First of all, through the average dwell time and piecewise Lyapunov function method, a su?cient exponential stability conditions is proposed for time-varying delay switched system of autonomous, use the jensen inequality and the reciprocally convex approach to do with the time-varying delay.Given the strict estimation of the system state decay. The condition is a LMI feasible solution problem. Then, using the above conditions, by system model transformation and some essential matrix transformation. Put forward a su?cient condition of the existence of reduced order sliding mode dynamics, and gives design method of the sliding surface parameters. The condition is a LMI non convex feasible solution problem, by the cone complementary linearization(CCL) method, we can transform this to a LMI minimization problem. Then, use sliding mode control input with known or unknown time-varying delay, forcing the state of closed-loop system to reach the sliding surface of pre designed.And for all subsequent time, the states of the closed-loop system is able to maintain on the sliding surface(continuous conditions), or remain near the preset sliding surface(discrete conditions). Finally, numerical examples of the continuous time and discrete time sliding mode control of switched systems with time-varying delay are given to demonstrate the e?ectiveness of the proposed theory.