Discrete sliding mode control for robust tracking of time-delay systems

This paper presents the discrete time sliding mode controller for the robust tracking of time-delay systems. In this, an optimal sliding surface is chosen as a linear function of the system-state error and the coefficients of sliding surface are computed by minimizing the quadratic performance index. A delay ahead predictor and corrector is used to handle system's time-delay and plant–model uncertainties. The control law is derived from the discrete time-state model and sliding surface with predicted states for general class of delay-time systems. The methodology integrates optimal sliding surface and delay ahead prediction; and therefore results in optimal performance of the systems. The stability condition is derived using the Lyapunov approach. Simulation examples are included to show the usefulness of the proposed controller.