This paper develops new results on iterative learning control of a class of spatially interconnected systems for the particular case of the passive or active electric ladder circuits. This task is performed by converting the problem to one of stability along the trial for a differential linear repetitive process, leading to design based on linear matrix inequality computations. In particular, sufficient conditions for the existence of a control law are developed together with the design algorithms for the associated controller matrices. Under this control law the resulting ILC dynamics have an asymptotic convergence in terms of an error sequence formed from the difference between both the distributed reference trajectory and the current trial output produced. Finally, an illustrative simulation is given to demonstrate the feasibility and effectiveness of the new designs.