An enhanced input-delay approach to sampled-data stabilization of T–S fuzzy systems via mixed convex combination

Abstract

The problem of sampled-data control is investigated for Takagi–Sugeno (T–S) fuzzy systems with aperiodic sampling intervals based on an enhanced input-delay approach. Delay-dependent stability and stabilizability conditions for the closed-loop continuous nonuniformly sampled-data fuzzy systems are derived by constructing a novel discontinuous Lyapunov–Krasovskii (L–K) functional, which makes good use of not only the upper bound on the variable sampling interval, but also its sawtooth structure information about varying input delay often ignored in previous results. A bounding technique combined by reciprocally convex technics and linear convex combination is presented for acquiring the time derivative of the functional, wherein Jensen’s inequality and Wirtinger’s inequality are integratively employed. And a feasible solution of the obtained criterion formulated as parameterized linear matrix inequalities is ultimately conceived. A numerical example is given to show the effectiveness of the proposed method.