A large class of discrete linear repetitive processes, termed discrete non-unit memory, can be interpreted as two-dimensional systems with the state-space model structure developed by Roesser. This paper shows that the criteria for stability along the pass of these repetitive processes is equivalent to BIBO stability for two-dimensional systems described by the Roesser model. The interplay of ideas between these two disciplines should greatly assist in the development of a coherent feedback control and systems theory for repetitive processes. Here, this new result is used to develop Lyapunov equations for discrete linear repetitive processes, which then yield new insight into their fundamental dynamic behaviour.