A minimum operator based discrete variable structure control

The objective of this article is to propose a reaching law for discrete variable structure control that utilizes a minimum operator based structure. The proposed solution has the features of modified Gao's method when the system states are distant with respect to the equilibrium point and Utkin's equivalent control -based method when states are in the vicinity of the equilibrium point. As a result, chattering is eradicated, and it is guaranteed that system states remain on the sliding manifold. Furthermore, it restricts the rate of change of the sliding variable by adjusting a gain. Consequently, for large initial conditions, the corresponding control input signal obtained is moderate with respect to that of Gao's reaching law. The design is explored for the system without perturbation, in which the sliding variable converges to the sliding manifold in finite -time steps and for the system influenced by the matched type bounded perturbation, in which the variable maintains itself in the vicinity of the manifold. To demonstrate the efficacy of the proposed reaching law, a numerical example and a perturbed pendulum system are considered.