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This paper investigates the ℓ2-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 on ℓ2-ℓ∞-disturbance attenuation is presented, in which both stability and prescribed ℓ2-ℓ∞ performance are required to be achieved for the filtering-error systems. Then, based on the condition, the full-order and reduced-order delay-dependent ℓ2-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

mathematical problems in engineering

A Novel Approach to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mi>ℓ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mi>ℓ</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mrow></mml:math>Filter Design for T-S Fuzzy Systems with Multiple Time-Varying Delays

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