Robust Stability and Stabilization for Uncertain Discrete-Time Fuzzy Systems with Time-Varying Delay

This paper discusses robust stability and stabilization of uncertain discrete-time fuzzy systems that have time-varying delay in state. There have been only a few results on stability and stabilization for discrete-time fuzzy time-delay systems. Especially, few results on robust stability and stabilization for a class of uncertain discrete-time fuzzy time-delay systems have appeared in the literature. Therefore, the study of robust stability and stabilization for uncertain discrete-time fuzzy time-delay systems is a very important problem. We first obtain a stability condition for nominal discrete-time fuzzy systems with time varying delay via linear matrix inequalities (LMIs). To this end, we define a new Lyapunov-Krasovskii function and use Leibniz-Newton formula and free weighting matrix method, which reduce the conservativeness and unnecessary LMI slack variables in our robust stability conditions. Then we extend to a robust stability condition for uncertain discrete-time fuzzy time-delay systems. Furthermore, we obtain a robustly stabilizing state feedback controller design method for uncertain fuzzy time-delay systems. Finally, we give some numerical examples to show the effectiveness of our conditions and to illustrate our design method.