On Realization Theory for Generalized State-Space Systems over a Commutative Ring

The problem of finding a state-space realization for a given rational matrix over a commutative ring is considered. To simplify the problem, we assume a certain factored structure for the denominator polynomials in the matrix. Our main results state that this class of matrices is a module which can be decomposed into two independent and isomorphic submodules, each realizable via existing results for strictly proper matrices. Any rational matrix with factored denominators can be realized through this decomposition.