A transformation for 2-D linear systems and a generalization of a theorem of Rosenbrock

The transformation of zero coprime system equivalence (z.c.s.e.) with its various characterizations is shown to have at least one important role for two dimensional linear systems theory. This paper shows that it is z.c.s.e. which forms the basis of the generalization of Rosenbrock's characterization of all least order polynomial realizations of a transfer function matrix for the case of 2-D systems. The definition of what consistutes the least order is shown to be crucial.