A Difference Equation With Minima-Based Reaching Law for Discrete Variable Structure Systems.

This paper deals with the design of discrete sliding mode control incorporating difference equation with minima. It discuss two reaching laws having hybrid structure with respect to Gao’s reaching law and Utkin’s reaching law. This approach overcomes the limitations of both methods, which are primarily chattering in the former and overly large control action in the latter case. These laws are crafted for systems with and without perturbation. In the case of the undisturbed system, the switching variable converges to zero within a finite-time steps, while for the perturbed system, the variable remains close to the vicinity of the switching manifold. Simulation results show the efficacy of the discussed methodology.