On the partial realization from two-dimensional input- output map

This note is concerned with a partial realization from a two-dimensional (2-D) input-output map where the Roesser´s model is used to represent 2-D systems. The problem considered here is to find a state-space model from a finite sequence which corresponds to a part of a 2-D input-output map. Since the case where the finite sequence satisfies certain rank conditions has been treated in the other paper, another case is the focus of the discussion in this note. A method is presented for extending a given finite sequence to a longer one until the rank conditions are satisfied, so that the order of a realized system is minimal in some sense.