Quantized Feedback Adaptive Reliable $$H_{infty }$$ Control for Linear Time-Varying Delayed Systems

Based on an improved (H_infty ) performance index, the method of designing a reliable adaptive (H_infty ) controller with quantized state is addressed for the time-varying delayed system in this paper. On the basis of online estimates of actuator faults, the controller parameters are updated automatically to compensate the influence of actuator faults on the system while the desired improved (H_infty ) performance is preserved. A Lyapunov function candidate is constructed to prove that the closed-loop system is asymptotically stable. And the existing sufficient conditions of the controller are proved to be less conservative. The gains of the controller and the parameters of the adaptive law are co-designed and obtained in terms of solutions to a set of linear matrix inequalities. Finally, two numerical examples are given to illustrate that the proposed method is more effective than the previous methods for time-varying delayed systems.