Hyperbolic tangent based switching reaching law for discrete time sliding mode control of dynamical systems

In this paper we consider the reaching law approach to the sliding mode control of discrete time systems. We present a reaching law based on the hyperbolic tangent trigonometric function. We begin by analyzing the case of nominal systems, and then extend the results to the problem of perturbed systems, that are subjected to disturbances and parameter uncertainties. We show, that for both scenarios the sliding mode controller designed according to the proposed reaching law enforces the quasi-sliding mode defined as changing the sign of the sliding variable in each consecutive control step, while maintaining its value in some a priori known vicinity of zero. We compare our solution to the most popular, constant plus proportional reaching law, and demonstrate, that it offers faster convergence and better robustness.