Repetitive processes are a distinct class of 2D systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by the direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. This article develops significant new results on the relationships between one physically motivated concept of controllability for the so-called discrete linear repetitive processes and the structure and design of control laws, including the case when disturbances are present.