A new algorithm for robust explicit/multi-parametric Model Predictive Control (MPC) for uncertain, linear discrete-time systems is proposed. Based on previous work on Dynamic Programming (DP), multi-parametric Programming and Robust Optimization, the proposed algorithm features, (i) a DP reformulations of the MPC optimization problem, (ii) a robust reformulation of the constraints, and (iii) a multi-parametric programming step, where the control variables are obtained as explicit functions of the state variable, such that the state and input constraints are satisfied for all admissible values of the uncertainty. A key feature of the proposed procedure is that, as opposed to previous methods, it only solves a convex multi-parametric programming problem for each stage of the DP procedure. (C) 2012 Elsevier Ltd. All rights reserved.