On irreducible factorization of rational matrices and their applications

This paper is an extension of the investigation of computational aspects of the spectral problems for a rational matrix from [4]. Methods of the solution of spectral problems for one- and two-parameter rational matrices are considered. The algorithms of constructing irreducible factorizations and among them a minimal factorization by degree and sizes of factors are suggested. Those algorithms allow us to reduce the spectral problems for rational matrices to the same problems for polynomial matrices. A relationship between the irreducible factorization and irreducible realization for a one-parameter matrix and its application in system theory is established. The results are extended to two-parameter rational matrices. Bibliography: 15 titles.