On the continuous-time Takagi–Sugeno fuzzy systems stability analysis

Abstract

In this paper, a new approach for the stability analysis of continuous-time Takagi–Sugeno (T-S) fuzzy system is proposed. The universe set is divided to subregions, and piecewise quadratic Lyapunov function is then found for each of them. This class of Lyapunov function candidates is much richer than the common quadratic Lyapunov function. By exploiting the piecewise continuous Lyapunov function, we derive stability conditions that can be verified via convex optimization over linear matrix inequalities (LMIs) or bilinear matrix inequalities (BMIs). These conditions are shown to be less conservative than some quadratic stabilization conditions published recently in the literature. Since this method uses low numbers of LMIs or BMIs and less computation Lyapunov functions, it is highly applicable and has less computation. This approach is not dependent on the shape of fuzzy sets and also, stability of the system is guaranteed in the presence of state feedbacks. At first, in order to decrease length of computation (amount of LMIs (BMIs)), an approach is introduced based on properties of the T-S system with two-overlapped fuzzy sets. Some criterions are obtained for stability analysis, stability analysis in the presence of parametric uncertainties and a stability criterion is presented to provide a reasonable performance for the system. To demonstrate the new approach, an illustrative example is presented.