A predictive regulator is described for stabilizing linear plants subject to polyhedral input constraints. While the asymptotic stability of general linear plants is ensured subject to a set-membership condition on the initial state, global asymptotic and semiglobal exponential regulation is achieved for input-saturated plants which are asymptotically null controllable with bounded inputs. The design knobs of the regulator can be chosen off line so as to compromise between nonconservative regulation performance and computational complexity, and an on-line optimization problem of prequantifiable numerical burden results.