A model reference adaptive variable structure controller for discrete system with time-delay

In this note, the original discrete uncertain system with time-delay is simplified to a discrete uncertain system without time-delay and a switching function is designed to guarantee that the movement of the system is asymptotically stable in the switching manifold. Then a discrete robust adaptive quasi-sliding-mode tracking controller is presented by the two given adaptive gains, and the globally asymptotically stability of the system is proved based on the Lyapunov stability theorem. Finally, an example and its simulation results are presented to illustrate the proposed approach.