This paper proposes a dynamic anti-windup scheme for a class of iterative learning control (ILC) systems. The anti-windup compensator has the same structure as a class of compensators for 1D systems and is able to guarantee similar properties: (i) that the constrained system with anti-windup compensation is exponentially stable if a certain linear matrix inequality is satisfied; and (ii) if the trajectory to be tracked by the nominal ILC controller is consistent with the control constraints, the anti-windup compensator will ensure that the behaviour of the nominal ILC controller is eventually recovered.