The practicality of model predictive control (MPC) is partially limited by its ability to solve optimization problems in real time. Moreover, on-line computational demand for synthesizing a robust MPC algorithm will likely grow significantly with the problem size. In this paper, we use the concept of an asymptotically stable invariant ellipsoid to develop a robust constrained MPC algorithm which gives a sequence of explicit control laws corresponding to a sequence of asymptotically stable invariant ellipsoids constructed off-line one within another in state space. This off-line approach can address a broad class of model uncertainty descriptions with guaranteed robust stability of the closed-loop system and substantial reduction of the on-line MPC computation. The controller design is illustrated with two examples. (C) 2003 Elsevier Science Ltd. All rights reserved.