On Matrix Fraction Representations for Linear Systems over Commutative Rings

This paper deals with the problem of existence of polynomial matrix fraction representations for transfer matrices of linear systems over rings as well as the related realization theory. These representations are then used in establishing new results for various classes of systems including split systems. The relevance of these results to the regulation of various “nonclassical” classes of linear systems (for example, delay-differential systems, two-dimensional systems, etc.) is also discussed.