A new method to address constrained robust model predictive control (MPC) for systems with polytopic description (RPC-SPD) is proposed. This is motivated by two previous techniques. One is the well-known robust MPC that parameterizes the infinite horizon control moves into a single linear state feedback law. The other is a nominal on-line MPC that splits the infinite horizon control moves into a set of free control moves over a fixed horizon and a state feedback law in the terminal region. The basic idea here is to adopt the rationale of the second technique to improve feasibility and optimality of the first one. A parameter-dependent Lyapunov function is developed for establishing the closed-loop stability. The performance of the controller is demonstrated by an example. (C) 2003 Elsevier Ltd. All rights reserved.