Title: On recursive computation of coprime factorizations of rational matrices,
Abstract: We propose general computational procedures based on descriptor state-space
realizations to compute coprime factorizations of rational matrices with
minimum degree denominators. Enhanced recursive pole dislocation techniques are
developed, which allow to successively place all poles of the factors into a
given "good" domain of the complex plane. The resulting McMillan degree of the
denominator factor is equal to the number of poles lying in the complementary
"bad" region and therefore is minimal. The new pole dislocation techniques are
employed to compute coprime factorizations with proper and stable factors of
arbitrary improper rational matrices and coprime factorizations with inner
denominators. The proposed algorithms work for arbitrary descriptor
representations, regardless they are stabilizable or detectable.