Discrete Uncertain Time-delay System Robust H_ ¡Þ Control

The paper considers the problems of robust H_∞control for uncertain discrete systems with time-varying delays.By choosing an improved Lyapunov function without ignoring some useful cross-terms and different free-weighting techniques,less conservative delay-dependent conditions for systems are obtained.The problem of H_∞control is equivalent to the feasibility of certain matrix inequalities.The matrix inequalities are solved to obtain the parameters of the controller by using the techniques of linear matrix inequality(LMI) and Matlab software.The studied subjects are following.(1) The problem of H_∞control for nonlinear uncertain discrete time systems via a state feedback controller is studied.Choosing the less conservative Lyapunov function,the state feedback controller and the original systems form a closed loop system.The sufficient conditions for stabilizability and H_∞control of the closed loop system are obtained respectively,including a set of linear matrix inequalities with an upper bound and a lower bound of the time delay.The parameters of the state feedback controller are obtained by solving linear matrix inequalities.(2) A class of uncertain linear systems with state delay is considered.In the condition of the unknown states of the system,we estimate the states of the system through the design of observer. Then the controller which is designed in the observer foundation not only causes the system to edge stably but also satisfies the H_∞performance.The obtained sufficient conditions for the existence of the controller transform the controller design question to the LMI solution question. By using the LMI toolbox in Matlab,It is easy to obtain the gain matrixes of the corresponding controller.(3) Designing of robust H_∞control of uncertain discrete time systems via output feedback is studied in this paper when the uncertainty in the system is assumed to be norm bounded and time varying.By defining new Lyapunov functions in terms of less conservativeness,it is proved that the existence of the H_∞control is equivalent to the feasibility of a certain matrix inequality. Due to nonlinear term,using of novel techniques of cone complementary linearization(CCL) and LMI solve the matrix to obtain parameters of the controller when the system satisfies the H_∞norm-bound.