Two different predictive control formulations are developed based on minimization of the worst-case quadratic cost for systems with bounded parameters. The two formulations differ on the assumptions made about the future inputs in optimizing the current input: one assumes open-leap control, while the other considers closed-loop control. Their closed-loop properties such as asymptotic stability are examined. We then focus on a moving average model with an integrator, and derive computationally simpler suboptimal algorithms. (C) 1997 Elsevier Science Ltd.