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In this paper, it is shown that any arbitrary 2-D polynomial system matrix can be reduced by zero coprime system equivalence to a generalized state space form. The exact form of both the generalized state space (GSS) system matrix and the transformation linking it to the original system matrix are established.
The connection between the polynomial matrix descriptions (PMD's) of the various singular 2D linear models is considered. It is shown that the transformation of zero coprime system equivalence provides the basis for the reduction of any given singular 2D general PMD to a singular Roesser form. The exact form of the transformation is established