Recursive computation of coprime factorizations

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.