Novel theory for polynomial and rational matrices at infinity. Part 2. Rational matrices

Abstract

The development reported in Part 1 of this series is continued by presenting a unifying theory for rational matrices at infinity. The cornerstone for the development is again the homogeneous form for polynomial and rational matrices. It is shown that when a rational matrix is factorized in matrix fraction description (MFD), redundancy at infinity may be introduced. This redundancy can be characterized precisely as the common divisor of the numerator and the denominator matrices at infinity. Moreover, when the numerator and the denominator matrices are completely coprime, the determinantal degree of the denominator is the McMillan degree of the rational matrix.