Discrete time sliding mode control for uncertain Delta operator systems with infrequent output measurements

A sliding mode control algorithm for discrete-time uncertain systems at higher sampling rates is proposed in this paper. The traditional shift operator based discrete-time systems at higher sampling rates fail to capture the dynamics of its continuous counter part, as the system matrix approaches to the identity matrix. To overcome this problem, the Delta operator has been used to represent the discrete system where the discrete system dynamics converges to the continuous system at higher sampling rates. Here, a periodic output feedback (POF) based sliding mode controller which makes use of infrequent output measurements is proposed to guarantee a stable sliding mode motion along a designed sliding surface for the Delta operator system. The design philosophy of this controller is to obtain the POF gain which will bring a sliding mode for the Delta operator system. It is shown here that there exists a POF gain for sliding mode to occur for any controllable and observable Delta operator system. Further, the sliding surface for this gain is derived. The design method is illustrated for an uncertain system with bounded matched uncertainty.