A discrete-time integral sliding mode control law for systems with matched and unmatched disturbances

This letter proposes a discrete-time integral sliding mode (DT-ISM) control strategy for linear time-invariant systems subject to matched and unmatched disturbances. The DT-ISM strategy is defined based on a discrete-time model of the system obtained from its continuous-time counterpart, providing numerical procedures to determine the sets in which the disturbances are contained, starting from the corresponding sets in the continuous-time domain. The DT-ISM law is based on disturbance estimation to ideally steer the sliding variable to zero in one discrete step, and achieves a quasi-DT-ISM in the presence of bounded estimation errors. The effectiveness of the proposed control law is tested in simulation combined with a robust model predictive control law.