Realizations of a state-space model from two-dimensional input-output map

This paper discusses the problem to realize an internal description from two-dimensional input-output map. First, for a class of Roesser´s model such that the denominator of the transfer function can be expressed by product of two polynomials of a variable, structure decomposition is carried out from the standpoint of separate local controllability and observability, and it is shown that the model is minimal if and only if it is separately locally controllable and observable. Next, the realization problem is formulated as the one of matching an infinite sequence of constant parameters which is equivalent to the input-output map and the model is used for the matching. For both cases where the matching is required over a finite number of terms of the sequence and It is required over the whole sequence, the existence conditions and the uniqueness of realizations are examined and an algorithm for finding a minimal realization within the model is presented.