In this paper an Iterative Learning Control (ILC) algorithm is proposed for a certain class of Linear Parameter Varying (LPV) systems whose dynamics change between iterations. Consistency of the algorithm in the presence of stochastic disturbances is shown. The proposed algorithm is tested in simulation and the obtained tracking performance is compared with that obtained using a standard Linear Time Invariant ILC algorithm. Better results are obtained using the proposed method. The method is also applied to a linear, permanent magnet synchronous motor system, which is shown to be an LPV system for a specific class of movements. Greatly improved tracking is achieved.