Minimal Factorization of Rational Matrix Functions

Abstract

In this chapter the notion of minimal factorization of rational matrix functions, which has its origin in mathematical system theory, is introduced and analyzed. In Section 9.1 minimal factorizations are identified as those factorizations that do not admit pole zero cancellation. Canonical factorization is an example of minimal factorization but the converse is not true. In Section 9.2 we use minimal factorization to extend the notion of canonical factorization to rational matrix functions that are allowed to have poles and zeros on the curve. In Section 9.3 (the final section of this chapter) the concept of a supporting projection is extended to finite-dimensional systems that are not necessarily biproper. This allows us to prove one of the main theorems of the first section also for proper rational matrix functions of which the value at infinity is singular.