Roesser model representation of 2D periodic behaviors: the (2,2)-periodic SISO case

In this paper we consider 2D single-input/single-output behaviors described by linear partial difference equations with (2,2)-periodically varying coefficients, and present a method to obtain 2D Roesser state-space representations (or realizations) for such behaviors. Since these cannot be obtained by separately realizing each shift-invariant system resulting from “freezing” the varying coefficients, we propose a method based on the realization of an invariant input/output behavior obtained by suitably “lifting” the trajectories of the original periodic behavior.