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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 devel- oped 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.
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 the desired FHM controllers are devel- oped in terms of linear matrix inequality (LMI). The designed controllers not only ensure that the closed-loop system is asymptotically stable but also a required H_ ∞ performance level. The matrices of the Lyapunov Krasovskii functional are not required to be diagonally positive-definitive.In addition, the traditional restriction that the derivative of the time-varying delay is strictly smaller than one is not needed. Before, the obtained results are less conservative. Finally, a simulation example is provided to show the effectiveness of the proposed methods.