Delay-dependent stability analysis and stabilization for T-S fuzzy models with time-delay

This paper proposed new generalized delay-dependent stability conditions of Takagi-Sugeno fuzzy time-delay systems. In the literature, both delay-independent stability conditions and delay-dependent stability conditions for fuzzy time-delay systems have already been obtained. However, those conditions are rather conservative and do not guarantee a wide stability region. Here we choose a generalized Lyapunov-Krasovskii functional and introduce a parameterized model transformation with free weighting matrices to it, in order to obtain generalized delay-dependent stability conditions. Our delay-dependent stability conditions thus obtained are given in terms of linear matrix inequalities (LMIs). Comparison with other stability conditions in the literature shows our conditions are the most powerful ones to guarantee the widest stability region. We also give example to illustrate our results, and the simulation results show that the LMI conditions based on the fuzzy Lyapunov function are less conservative than those based on a common (standard) Lyapunov function.