Delay-dependent H∞ Control for T-S Fuzzy Systems Based on a Switching Fuzzy Model and Piecewise Lyapunov Function

Abstract

This paper studies the problem of H ∞ control for discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delays. The T-S fuzzy system is transformed to an equivalent switching fuzzy system. Consequently, the delay-dependent stabilization criteria with H ∞ performance are derived for the switching fuzzy systems based on the piecewise Lyapunov function. The proposed conditions are given in terms of linear matrix inequalities (LMIs). The interactions among the fuzzy subsystems are considered in each subregion, and accordingly the proposed conditions are less conservative than the previous results. Finally, a design example is given to show the validity of the proposed method.