Relaxed H-infinity Stabilization Conditions for Discrete-Time Fuzzy Systems With Interval Time-Varying Delays

Abstract

To derive less-conservative delay-and range-dependent H-infinity stabilization conditions for discrete-time Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays, the use of a fuzzy-weighting dependent Lyapunov-Krasovskii functional (FWLKF), in which all variables are set to be affinely or quadratically dependent on fuzzy weighting functions, is proposed. Subsequently, parameterized linear matrix inequality (PLMI)-based H-infinity stabilization conditions are derived by following the free-weighting matrix approach. To fully exploit the convexity of fuzzy weighting functions, the derived PLMIs are sequentially replaced by a finite set of LMIs by considering all possible conditions associated with fuzzy weighting functions.