New delay-dependent approach to robust stability and stabilization for Takagi–Sugeno fuzzy time-delay systems

Abstract

In this paper, we consider 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. This is also true in case of the robust stability for uncertain fuzzy time-delay systems. Here we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, in order to obtain generalized delay-dependent stability conditions. In fact, these techniques lead to generalized and less conservative stability conditions that guarantee a wide stability region. Our delay-dependent stability conditions thus obtained are given in terms of linear matrix inequalities (LMIs). We give three examples to illustrate our results. Comparison with other stability conditions in the literature shows our conditions are the most powerful ones to guarantee the widest stability region. We also consider the robust stability of fuzzy time-delay systems with uncertain parameters. Applying the same techniques obtained for the stability conditions, we obtain delay-dependent sufficient conditions for the robust stability of uncertain fuzzy systems. Moreover, we give a design method of robustly stabilizing controllers for uncertain Takagi–Sugeno fuzzy time-delay systems.