A new approach to stability analysis and stabilization of discrete-time T-S fuzzy time-varying delay systems.

This paper investigates the problems of stability analysis and stabilization for a class of discrete-time Takagi-Sugeno fuzzy systems with time-varying state delay. Based on a novel fuzzy Lyapunov-Krasovskii functional, a delay partitioning method has been developed for the delay-dependent stability analysis of fuzzy time-varying state delay systems. As a result of the novel idea of delay partitioning, the proposed stability condition is much less conservative than most of the existing results. A delay-dependent stabilization approach based on a nonparallel distributed compensation scheme is given for the closed-loop fuzzy systems. The proposed stability and stabilization conditions are formulated in the form of linear matrix inequalities (LMIs), which can be solved readily by using existing LMI optimization techniques. Finally, two illustrative examples are provided to demonstrate the effectiveness of the techniques proposed in this paper.