Minimal factorization of rational matrices

A factorization of a regular rational matrix R(¿) = R1 (¿)R2 (¿) is said to be minimal if the degrees ¿1 and ¿2 of the two factors add up to the degree ¿ of R(¿). This problem has been studied earlier and it is known that in general nontrivial (i.e. ¿1¿0 and ¿2;¿0) factorizations may not exist [1]. Recently [2-3] a geometric approach using state-space representations yielded simple existence conditions for general minimal factorizations. In this paper we follow a more practical approach and focus on numerical and algorithmic aspects. Since the two points of view complement each other we briefly recall the main results of [3] from a system theoretical perspective.