Robust sliding mode learning control for uncertain discrete-time multi-input multi-output systems

A robust sliding mode-based learning control scheme is newly developed for a class of uncertain discrete-time multi-input multi-output systems. In particular, a recursive-learning controller is designed to enforce the sliding variable vector to reach and remain on the intersection of the sliding surfaces, and the system dynamics is then guaranteed to asymptotically converge to zero on the pre-described sliding manifold with respect to uncertainty. The 'Lipschitz-like condition' for sliding mode control systems, which presents an essential property of the continuity of uncertain systems, is further extended to the discrete-time case establishing in this study. The appealing attributes of this approach include: (i) the knowledge of the bounds of the uncertainties is not required for the controller design, (ii) the closed-loop system exhibits a strong robustness against uncertain dynamics and (iii) the control scheme enjoys the chattering-free characteristic. Simulation results are given to illustrate the effectiveness of the proposed control technique.