In this paper we are interested in the computation of feasible sets for linear model predictive control techniques, based on set relations and not on the conventional orthogonal projection. Further, the problem of computing suitable inner approximations of the feasible sets is considered. Such approximations are characterized by simpler polytopic representations, and preserve essential properties as convexity, positive invariance, inclusion of the set of expected initial states. (C) 2010 Elsevier Ltd. All rights reserved.