Relaxed delay-dependent stabilization conditions for discrete-time fuzzy systems with time delays

Abstract

Based on fuzzy weighting-dependent Lyapunov-Krasovskii functional (FWLKF), this paper proposes a method of designing a delay-dependent fuzzy controller for discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delays. To derive a less conservative delay-dependent stabilization condition, the method enhances the interactions among the fuzz subsystems using FWLKF with quadratic dependence on fuzzy weighting functions, where all the decision variables of FWLKF are set to be associated with the fuzzy weighting functions. Besides, this paper sets the overall controller to be dependent on not only the current-time but also the delay-time information on the fuzzy weighting functions. In the derivation, the stabilization condition is first formulated in terms of parameterized linear matrix inequalities (PLMIs), and then is reconverted LMIs based on several relaxation techniques.