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

In this paper, the method for obtaining of 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 too, One also throw some new light on the problem of the mutual connections among the different 2-D state-space models as the Roesser, the Fornasini-Marchesini, and the general one. Singular as well as the standard (nonsingular) models are considered.