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On the relation between stable matrix fraction factorizations and regulable realizations of linear systems over rings

Various types of transfer matrix factorizations are of interest when designing regulators for generalized types of linear systems (delay differential, 2D, families of systems). This paper studies the existence of stable and of stable proper factorizations, in the context of the theory of systems over rings. Factorability is related to stabilizability and detectability properties of realizations of the transfer matrix.