Discrete sliding mode control based on optimal sliding surface for time delay systems

This paper addresses the controller design problem of time delay systems using discrete sliding mode control technique. In this, an optimal sliding surface is chosen as a linear function of the system states and the coefficients of sliding surface are computed by minimizing the quadratic performance index. A delay ahead predictor is used to handle system´s time delay and plant-model uncertainties by predicting the states of systems. 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 optimal performance of the systems. The stability condition is derived using Lyapunov approach. Simulation examples are included to show the usefulness of the proposed controllers.