Exponential Stability And Robust H_∞ Control For Discrete-time Systems With Delays

This paper considers the exponential stability and robust H_∞control problems for discrete-time systems with time-varying delays, Based on the Lyapunov stability theory and free-weight matrix method, we obtain the exponential stability criteria and the sufficient condition for the existence of H_∞controller, which are expressed in linear matrix inequalities.In chapter one, we firstly introduce the background related to the content of this paper, then present several lemmas which will be used in this paper.In chapter two, the exponential stability is considered for the uncertain discrete-time systems with nonlinear disturbance and time-varying delay. Based on the Lyapunov stability theory and free-weight matrix method, delay-dependent exponential stability criteria are derived. Finally, numerical examples are given to show the effectiveness and feasibility of derived results.In chapter three, the robust H_∞control problem is considered for a class of uncertain discrete-time systems with time-varying delay. Based on the Lyapunov stability theory, and by using new method for estimating the upper bound of the difference of Lyapunov functional, the new sufficient conditions for the existence of H_∞controller are obtained. Finally, several numerical examples are presented to show the effectiveness and less con-servativeness of obtained results.