This paper considers iterative learning control for the practically relevant case of deterministic discrete linear plants where the first Markov parameter is zero. A 2D systems approach that uses a strong form of stability for linear repetitive processes is used to develop a one step control law design for both trial-to-trial error convergence and along the trial performance. The resulting design computations are completed using linear matrix inequalities, and results from applying the control law to one axis of a gantry robot are also given by way of experimental verification.