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Repetitive processes are a distinct class of two-dimensional (2D) systems (i.e. information propagation in two independent directions occurs) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or (often) 2D systems theory. In this paper we begin the development a systems theory for a model of these processes necessary to represent terms which arise in some applications areas but are not included in the currently used models.