In this article, a discrete-time sliding mode control law is proposed for nonlinear (possibly multiinput) systems, in the presence of mixed input-state constraints and additive bounded disturbances. The control law is defined by formulating a nonlinear predictive control problem aimed at generating a control input that imitates an unconstrained discrete-time sliding mode law. In addition to satisfying input and state constraints, the resulting control law has all the properties of discrete-time sliding mode, and in particular, finite time convergence of the state onto the sliding manifold in the nominal case, or into an a-priori defined boundary layer of the sliding manifold in case bounded disturbances are present.
