  General computational methods based on descriptor state-space realizations
are proposed to compute coprime factorizations of rational matrices with
minimum degree denominators. The new methods rely on recursive pole dislocation
techniques, which allow to successively place all poles of the factors into a
"good" region 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 developed pole dislocation
techniques are instrumental for devising numerically reliable procedures for
the computation of coprime factorizations with proper and stable factors of
arbitrary improper rational matrices and coprime factorizations with inner
denominators. Implementation aspects of the proposed algorithms are discussed
and illustrative examples are given.
