This paper presents the design of iterative learning control based on quadratic performance criterion (Q-ILC) for linear systems subject to additive uncertainty. The robust Q-ILC design can be cast as a min-max problem. We propose a novel approach which employs an upper bound of the worst-case performance, then formulates a non-convex quadratic minimization problem to get the update of iterative control inputs. Applying Lagrange duality, the Lagrange dual function of the non-convex quadratic problem is equivalent to a convex optimization over linear matrix inequalities (LMIs). An LMI algorithm with convergence properties is then given for the robust Q-ILC design. Finally, we provide a numerical example to illustrate the effectiveness of the proposed method. (C) 2008 Elsevier Ltd. All rights reserved.