Sliding mode control of discrete-time switched systems subject to mode delays

This work considers the sliding mode control problem of a class of discrete-time uncertain switched systems subject to detecting-delay on mode signals, which may result in the asynchronous phenomenon between the controller and the switched system. Since the mode information of the controlled system is not available for the controller in time, a mode-independent sliding surface will be introduced, by which an asynchronous sliding mode controller is designed, whose control gain and robust parameter will be changing according to the controller mode. In the analysis on the stability of the closed-loop control system and the reachability of the specified sliding surface, the asynchronous characteristics are detailedly investigated. It is shown that the Lyapunov function may be not always decreasing along the state trajectories during the unmatched interval of controller modes and system modes. Nevertheless, it is proven that the state trajectories can be driven into a sliding region around the specified sliding surface in finite time. Finally, some numerical simulation results are provided.