Elementary operation approach to state-space realizations of 2-D systems

In this paper, the method for obtaining various state-space realizations of the Roesser type for an assigned two-variable transfer function is developed. Two-variable elementary polynomial operations are employed. A new version of the general, state-space model is constructed. One also throws some new light on the problem of the mutual connections among the different 2-D state-space models such as the Roesser, the Fornasini-Marchesini, and the general one. Singular as well as standard (nonsingular) models are considered.