Asynchronous Stabilization of Switched Singular Systems with Interval Time-Varying Delays

This paper concerns the asynchronous stabilization problem of switched singular systems with interval time-varying delays. In ideal cases, the stabilizing controller is designed under the assumption that the switching times between the system and the controller are exactly the same. In fact, there are time-delays in the switching signal of the controller, which results in asynchronous switching. The closed-loop system may be unstable under the average dwell time and the controllers derived by ignoring the switching delay. For this case, based on piecewise Lyapunov-Krasovskii functional technique and merging signal method, some sufficient conditions for existence of a stabilizing controller are provided to guarantee that the switched singular time-delay system is regular, impulse free, and exponentially stable with the new average dwell time conditions. Then, the stabilizing controller depending on the asynchronous information is designed. Finally, a numerical example is given to demonstrate the effectiveness of the results.