New relaxed stability and stabilization conditions for T‐S fuzzy systems with time‐varying delays

Abstract

This paper investigates the stability analysis and stabilization of T-S fuzzy systems with time-varying delays. First, a new augmented Lyapunov–Krasovskii functional is constructed, delay-dependent stability criteria in terms of linear matrix inequalities (LMIs) are obtained by combining them with the integral inequality technique and the reciprocally convex combination inequality. Based on the state space decomposition method, some piecewise membership functions are employed to approximate the membership functions. The piecewise membership functions can be locally represented in terms of the convex combinations of the supremum and infimum of some local basis functions. The boundary information of the membership functions is adequately taken into consideration in stability analysis, and then some relaxed membership-function-dependent stability results are obtained. Second, state feedback controllers for fuzzy systems with time-varying delays are presented under the imperfect premise-matching technique, whose membership functions and the number of fuzzy rules are allowed to be designed freely, consequently, the flexibility of controller design is improved. Finally, four numerical examples are given to demonstrate the effectiveness of the presented approaches.