Generalized ℋ2 control for delayed discrete-time fuzzy systems via a delay-dependent approach

This paper provides a delay-dependent approach to the design of generalized H₂ state-feedback fuzzy controllers for discrete-time T-S fuzzy systems with both state and input delays. The delays are assumed to be time varying and bounded in an interval. Firstly, a fuzzy-basis-dependent functional is proposed, which yields a delay-dependent condition ensuring the stability as well as the generalized H₂ performance of the resulting closed-loop system. Secondly, a delay-dependent condition for the existence of desired controllers is presented by means of relaxed linear matrix inequalities (LMIs). When these LMIs are feasible, a desired fuzzy controller can be easily constructed. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed design method.