Physically realistic step function control rod models are shown to be unsolvable under traditional formulations of distributed parameter optimal control theory. Extensions to the theory are proposed and derived to allow these systems to be analyzed using straightforward optimality conditions. The extended theory is then applied to a xenon-iodine oscillation problem in two dimensions. The conditions of optimality are found, and analytical insights concerning the importance of the control rod tip for the optimality condition are obtained. The flux influence function is found by solving an eigenvalue problem, and the required normalization condition is found in one of the optimality conditions. The optimality and normalization conditions are solved numerically for a severe xenon transient, and the transient is stabilized by the intervention of the optimal control.