Abstract
Abstract. We propose a new computational approach based on descriptor state space algorithms to compute normalized coprime factorizations of rational matrices.

Since the initial reduction can lead to unnecessary accuracy loss, this approach raises serious concerns from numerical point of view. For discrete-time systems, apparently t,here are no results for non-proper TFMs.

In this paper we propose a completely general method to compute NRCFs of arbitrary continuous-or discretetime TFMs. The procedure given below can be seen as a constructive proof of the following main result. Step 1 reduces essentially the NRCF problem to one for a proper TFM. This step can be performed by using an algorithm proposed in [2] . The NRCF is computed at steps 2 and 3 by solving a spectral factorization problem for a proper system in a descriptor representation with nonsingular E. This can be done by solving appropriate descriptor Riccati equations arising from the descriptor variants of standard spectral factorization algorithms. From numerical point of view, the proposed approach represents a completely satisfactory computational solution to determine NRCFs. Applied to G T , it can be equally used to compute normalized left coprime factorizations too. By applying an appropriate orthogonal similarity transformation, the given system matrices can be put in a SVD-like coordinate form

where Ell E Rrxr is nonsingular. Because of minimality assumption, rank B2 = n -r and we can take and, respectively, the ertended simplectic pencil (ESP)

The 

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