Coprime factorizations of transfer matrices for linear systems over rings

This paper develops a general factorization theory of transfer matrices for linear systems defined over rings. Restricting the rings to the class of unique factorization domains (UFDs) and introducing a notion of denominator sets, a coprime right (left) factorization for the transfer matrix of a system over a UFD is studied. Various properties of coprime factorizations are obtained. In particular, the coprimeness is characterized in terms of algebraic properties of the factor matrices. The results obtained are applied to the problem of realising a precompensator by state feedback