Discrete time integral sliding-mode control for systems with matched and unmatched uncertainties

A new chattering-free integral sliding-mode control method is proposed for discrete-time linear systems with unmatched uncertainties. Based on the linear matrix inequality (LMI) technique, a new sliding-mode switching function is proposed. The effect of unmatched uncertainties is minimized, and the Lyapunov stability is proved. Then the sliding mode controller is proposed. The saturation function is introduced to ensure that the system states move in a small neighborhood of the sliding surface as quasi-sliding motion. The boundary layer thickness of the saturation function is chosen to make sure the controller is chattering-free with strong robustness. The theoretical analysis and simulation results show the effectiveness of the proposed integral sliding-mode control scheme.