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.