A Schur Method for Computing Coprime Factorizations with Inner Denominators and Applications in Model Reduction

The paper presents a numerically reliable algorithm for computing minimal order rational coprime factorizations with inner denominators of transfer-function matrices. The proposed algorithm constructs the inner denominator sequentially asd a product of first or second order elementary inner factors by using an efficient Schur form updating technique. The algorithm is generally applicable regardless the state-space representation of the given transfer-function matrix is minimal or not, or is stabilizable/detectable or not. The resulting factorization is in a particular form which is well suited to be further employed in coprime factors model reductions or for computing 2-norms of unstable transfer-function matrices.