A Novel Approach toℓ2-ℓ∞Filter Design for T-S Fuzzy Systems with Multiple Time-Varying Delays

Abstract

This paper investigates theℓ2-ℓ∞filtering problem of T-S fuzzy systems with multiple time-varying delays. First, by the Lyapunov-Krasovskii functional approach and free-weighting matrix method, a delay-dependent sufficient condition onℓ2-ℓ∞-disturbance attenuation is presented, in which both stability and prescribedℓ2-ℓ∞performance are required to be achieved for the filtering-error systems. Then, based on the condition, the full-order and reduced-order delay-dependentℓ2-ℓ∞filter design schemes for T-S fuzzy multiple time-varying delays systems are developed in terms of linear matrix inequality (LMI). Finally, an example is given to illustrate the effectiveness of the result.