In this paper, we propose a new robust MPC method that guarantees stability and offset-free set point tracking in the presence of model uncertainty. A min-max optimization problem that explicitly accounts for model uncertainty is used to determine the optimal control action subject to the input and output constraints. The robust regulator uses a tree trajectory to forecast the time-varying model uncertainty. The controller design procedure uses integrators to reject non-zero disturbances and maintain the process at the optimal operating conditions (set points). Constraints may cause offset, which occurs when the set points are unreachable. In the feasible region where constraints are not active, the robust MPC theory we propose achieves offset-free non-zero set point tracking if there exists a control policy that robustly stabilizes all models in the uncertainty set. (C) 2003 Elsevier Ltd. All rights reserved.