Anti-windup control of discrete time switched delay systems with actuator saturation and failures.

The problem of L-gain analysis and anti-windup (AW) fault-tolerant controller design of a class of time-varying delay discrete-time switched systems with actuator saturation and external disturbances is investigated by using the multiple Lyapunov functionals method. Firstly, for each subsystem, we construct an AW fault-tolerant controller consisting of a dynamic state feedback (DSF) controller and an AW compensator, such that the closed-loop system with actuator faults can meet the disturbance attenuation performance index and ensure that the state trajectories of the closed-loop system are bounded under the action of external disturbances. Then, the problem of estimating the allowable interference capacity is transformed into a constrained optimization problem. Next, a sufficient condition on the existence of the restricted L-gain is established, and the minimum upper bound of the restricted L-gain is obtained by solving the constrained optimization problem. Finally, the DSF controller gain and AW compensator gain of the AW fault-tolerant controller are obtained by solving the above two optimization problems which have been further handled. A numerical example is given to show the effectiveness and feasibility of the proposed method.