Delay-Dependent Generalized H2 Control for Discrete-Time T-S Fuzzy Systems Based on a Switching Fuzzy Model and Piecewise Lyapunov Function

This paper studies the problem of generalized H₂ control for discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delays. First, the T-S fuzzy system is transformed to an equivalent switching fuzzy systems. Consequently, based on the piecewise Lyapunov function, the delay-dependent stabilization criteria with generalized H₂ performance are derived for the switching fuzzy systems.The proposed conditions are presented in terms of linear matrix inequalities (LMIs). The interactions among the fuzzy subsystems are considered in each subregion. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. To illustrate the validity of the proposed method, a design example is provided.