On computing normalized coprime factorization of arbitrary rational matrices

We present a numerically reliable approach for computing the normalized coprime factorization of an arbitrary (possibly improper) rational matrix. We consider both the cases in which the factorization is coprime and normalized with respect to either the left half plane or the unit disk, corresponding to systems with continuous or discrete-time evolutions. The proposed algorithms remedy some numerical drawbacks of alternative methods available so far in the literature.