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This paper is concerned with the design of stabilizing model predictive control (MPC) laws for constrained linear systems. This is achieved by obtaining a suitable terminal cost and terminal constraint using a satu-rating control law as local controller. The system controlled by the saturating control law is modelled by a linear difference inclusion. Based on this, how to determine a Lyapunov function and a polyhedral invariant set which can be used as terminal cost and constraint is shown. The obtained invariant set is potentially larger than the maximal invariant set for the unsaturated linear controller, O∞. Furthermore, considering these elements, a simple dual MPC strategy is proposed. This dual-mode controller guarantees the enlargement of the domain of attraction or, equivalently, the reduction of the prediction horizon for a given initial state. If the local control law is the saturating linear quadratic regulator (LQR) controller, then the proposed dual-mode MPC controller retains the local infinite-horizon optimality. Finally, an illustrative example is given