Robust H∞ control based on fuzzy hyperbolic model with time-delay

This paper investigates the problems of robust stabilization and robust H∞ control for the fuzzy hyperbolic model (FHM) with time-varying delay. A kind of novel Lyapunov–Krasovskii functional is constructed. By using the descriptor model transformation and free-weighting matrix technique, new delay-dependent sufficient conditions for the existence of desired FHM controllers are developed in terms of linear matrix inequality (LMI). The designed controllers not only ensure that the closed-loop system is asymptotically stable, but also satisfy a prescribed H∞ performance level. The matrices of the Lyapunov–Krasovskii functional are not required to be diagonally positive-definite. In addition, the traditional restriction that the derivative of the time-varying delay is strictly smaller than one is not needed. Therefore, the obtained results are less conservative. Finally, a simulation example is provided to show the effectiveness of the proposed methods.