Abstract
This paper proposes a discrete-time sliding mode control (DSMC) strategy for linear (possibly multi-input) systems with additive bounded disturbances, which guarantees the satisfaction of input and state constraints. The control law is generated by solving a finite-horizon optimal control problem at each sampling instant, aimed at obtaining a control variable that is as close as possible to a reference DSMC law, but at the same time enforces constraint satisfaction for all admissible disturbance values. Contrary to previously-proposed control approaches merging DSMC and model predictive control, our proposal guarantees the satisfaction of all standard properties of DSMC, and in particular the finite-time convergence of the state into a boundary layer of the sliding manifold.