Several predictive control strategies that handle input/output constraints have been proposed in the literature. The difficulty with all these approaches is that, in an attempt to optimize output tracking over a finite horizon, they tend to drive the controls to the constraint limits; this can lead to infeasibility, which, in the case of systems with poles and/or zeros outside the unit circle, leads to instability. The aim of this paper is to develop necessary and sufficient conditions for feasibility and stability and to propose an algorithm that overcomes finite-horizon infeasibility and gives stability and asymptotic tracking.