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Iterative Learning Control (ILC) is now well established for linear and nonlinear dynamics in terms of both the underlying theory and experimental application. This approach is specifically targeted at applications where the same operation is repeated over a finite duration with resetting between successive executions. Each execution is known as a trial and the novel principle behind ILC is to suitably use information from previous trials in the selection of the current trial input with the objective of sequentially improving performance from trial-to-trial. In this paper, new results on the extension of the ILC approach to the class of 2D systems that arise from certain methods of discretization of partial differential equations, resulting in the need to use a spatio-temporal setting for analysis. The resulting control laws can be computed using Linear Matrix Inequalities (LMIs). An illustrative example is also given and areas for further research discussed.