Computation of coprime factorizations of rational matrices

We propose numerically reliable state-space algorithms for computing several coprime factorizations of rational matrices: (1) factorizations with factors having poles in a given stability domain; (2) factorizations with proper stable factors; (3) factorizations with inner and J-inner denominators. The new algorithms are based on a recursive generalized Schur algorithm for pole dislocation. They are generally applicable whether the underlying descriptor state-space representation is minimal or not, and whether it is stabilizable/detectable or not. The proposed algorithms are useful in solving various computational problems for both standard and descriptor system representations.