Composite anti-disturbance control for a discrete-time time-varying delay system with actuator failures based on a switching method and a disturbance observer

•The system is transformed to a switched system based on the information of actuator failures.•A disturbance observer is constructed to estimate the disturbances.•Combining disturbance observer and exponential l2−l∞l2−l∞ performance index, a controller is given.

The composite anti-disturbance control problem is developed for discrete-time systems with both time-varying delay and multiple disturbances under actuator failures in this paper. First, depending on the information of actuator failures, the system is transformed into a switched system. Then, considering the switched system, the composite controller is designed via a disturbance observer based control and an exponential l2−l∞l2−l∞ control method. A disturbance observer is constructed to estimate the disturbances generated by an exogenous system, and the estimated value is introduced into a memory exponential l2−l∞l2−l∞ state feedback control law, such that, the closed-loop system is asymptotically stable, and different types of disturbances are rejected and attenuated. Third, by resorting to the average dwell time approach and the free-weighting matrix technique, some sufficient criteria for the desired disturbance observer and the state feedback controller are established, and the corresponding solvability conditions using a cone complementarity linearization method are presented. A numerical example is provided to demonstrate the effectiveness of the proposed algorithms finally.