An Improved Approach to Delay-dependent Stability Analysis and Stabilization for Takagi-Sugeuo Fuzzy Models with Time-delay

This paper focuses on the improved approach problem for delay-dependent stability analysis and controller synthesis of T-S fuzzy systems with time delay. We first consider asymptotical stability conditions of fuzzy systems. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time delay, and are given in linear matrix inequalities (LMIs). An appropriate selection of Lyapunov-Krasovskii function and introduction of integral inequality approach (ⅡA) generalize asymptotical stability conditions. Next, we consider the stabilization problem with memoryless and delayed feedback controllers. The LMI optimization approaches are used to obtain a sufficient condition that is very easy to be checked by using the LMI Toolbox in Matlab. Based on them, we can obtain the maximum allowable delay bound (MADB). Finally, we give two examples that illustrate our results. We compare our conditions with other stability conditions and show our conditions are rather generalized.