Output feedback variable structure control for uncertain time-varying delay systems — Descriptor system approach

In this paper, the static output feedback variable structure control for uncertain time-varying delay systems is discussed based on a descriptor system approach. First, based on stability theory of descriptor time-varying delay systems, a linear matrix inequality sufficient condition which guarantees that the sliding mode dynamics is robust stable and the switching surface is existent is given. Then, the design method of a static output feedback variable structure controller is given, which guarantees that the closed-loop system is robust asymptotically stable, and the state trajectories of the closed-loop system are convergent to the switching surface in finite time. Last, a numerical example is given to show the correctness and effectiveness of the proposed method.