Abstract: The robust H_∞ stability control problem is considered for a class of discrete uncertain fuzzy system with time-delay. Based on the fuzzy Lyapunov-Krasovskii function (LFK), a fuzzy controller is designed to acquire globally asymptotical stability for the discrete uncertain fuzzy time-delay system with the method of parallel distributed compensation (PDC). Then a new sufficient condition for checking the stability of the closed-loop fuzzy system is proposed and proved. The controller design involves solving a set of linear matrix inequalities (LMIs) by introducing multiply additional matrix variables. Due to the idea of fuzzy LKF, the obtained robust stability condition has less conservativeness than the one based on the common LKF. A simulation example shows that the approach is effective.

Key words: discrete time control systems, fuzzy Lyapunov-Krasovskii function, fuzzy control, asymptotic stability, linear matrix inequality