A novel approach to \(\ell_2\)-\(\ell_\infty\) filter design for T-S fuzzy systems with multiple time-varying delays (Q459730)

Summary: This paper investigates the \(\ell_2\)-\(\ell_\infty\) 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 \(\ell_2\)-\(\ell_\infty\)-disturbance attenuation is presented, in which both stability and prescribed \(\ell_2\)-\(\ell_\infty\) performance are required to be achieved for the filtering-error systems. Then, based on the condition, the full-order and reduced-order delay-dependent \(\ell_2\)-\(\ell_\infty\) 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.