A general switching type reaching law for discrete time sliding mode control systems

In this paper sliding mode control of discrete time systems based on the reaching law approach is considered. In the quasi-sliding mode, the representative point of the controlled system is required to cross the sliding hyperplane in each successive sampling step and to remain in a known a priori vicinity of the hyperplane. We present a generic reaching law which is a generalization of a few previously known solutions. We begin by analyzing the case of nominal systems, and then we extend the results to perturbed systems that are subject to parameter uncertainties and external disturbances. For both cases we demonstrate the conditions that the reaching law must satisfy, in order to enforce the quasi-sliding motion in the system.