Membership-function-dependent control of fuzzy systems with time-varying delays

Abstract:

This paper investigates the stability analysis and stabilization for T-S fuzzy systems with time-varying delays. Firstly, an augmented Lyapunov-Krasovskii functional is constructed, delay-dependent stability criteria in terms of linear matrix inequalities (LMIs) are obtained by combining with the free-matrix-based integral inequality. Based on the state space decomposition method, some piecewise membership functions are employed to approximate the membership functions, which 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 taken into consideration adequately, meanwhile, some slack matrices are employed, and then some relaxed membership-function-dependent stability results are obtained. Secondly, state feedback controllers for the 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, two numerical examples are given to demonstrate the effectiveness of the presented approaches.