Coprime factorization with J all-pass denominator: The noncanonical case

Given an arbitrary rational matrix G, we are interested to construct the class of coprime factorizations of G with J-all pass denominators of McMillan degree as small as possible. Recently, we have given necessary and sufficient solvability conditions and a construction of the class of solutions in the canonical case in which the denominator has McMillan degree equal to the number of unstable poles of G. In this paper we extend the theory of co-prime factorizations with minimal degree denominator to the noncanonical case.