On recursive computation of coprime factorizations of rational matrices
For control theory and systems engineering, this provides numerically reliable procedures for computing coprime factorizations, though the contribution is incremental.
The paper proposes recursive computational methods for coprime factorizations of rational matrices, achieving minimal McMillan degree denominators by placing poles in a 'good' region. The methods are demonstrated with illustrative examples.
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.