Minimal factorization of rational matrices

A factorization of a regular rational matrix R(λ) = R1 (λ)R2 (λ) is said to be minimal if the degrees δ1 and δ2 of the two factors add up to the degree δ of R(δ). This problem has been studied earlier and it is known that in general nontrivial (i.e. δ1δ0 and δ2;≠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.