This paper deals with the development of a robust model predictive control strategy with guarantee of stability, applicable to the stable and unstable processes. The model uncertainty is assumed to be described by a discrete set of linear models (multi-plant uncertainty), and the robustness is achieved by assembling cost-contracting constraints for all the possible models in the uncertainty domain. On the basis of a suitable state-space model description, an offset free control law is obtained by means of a one-step optimization formulation. The usefulness of the method proposed here is illustrated with control simulations of an unstable reactor system taken from the literature. (C) 2016 Elsevier Ltd. All rights reserved.