This paper addresses the synthesis approach for output feedback robust model predictive control for systems with polytopic description, bounded state disturbance and measurement noise. Off-line, it calculates a sequence of output feedback laws based on the state estimators, by solving linear matrix inequality (LMI) optimization problems. On-line, at each sampling time, it chooses an appropriate output feedback law from this sequence. The primary contribution is to present a rigorous method to guarantee satisfaction of input/state constraints. A numerical example is given to illustrate the effectiveness of the controller. (c) 2007 Elsevier Ltd. All rights reserved.