Robust $H_{\infty}$ Control for Uncertain Takagi–Sugeno Fuzzy Systems With Interval Time-Varying Delay

This paper is concerned with the problem of robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin </sub> control for a class of uncertain time-delay fuzzy systems. The time-delay is assumed to be a time-varying continuous function belonging to a given interval, which means that the lower and upper bounds for the time-varying delay are available. No restriction on the derivative of the time-varying delay is needed, which allows the time-delay to be a fast time-varying function. The Takagi-Sugeno (T-S) uncertain fuzzy model with interval time-varying delay is adopted. Based on the Lyapunov-Krasovskii functional approach, some delay-dependent conditions for the existence of robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> controller are formulated in the form of linear matrix inequalities (LMIs). When these LMIs are feasible, an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> controller is presented. A numerical example is given to demonstrate the effectiveness of the proposed method