Rational Inner and Outer Functions

Abstract

Rational transfer functions naturally occur in many practical systems and control problems. Recall that a function admits a finite dimensional state space realization if and only if it is proper and rational. The finite dimensional state space setting is ideal for using computers to design feedback controllers and analyzing transfer functions. In this chapter, we will use state space realizations to characterize inner and outer rational functions. We will also present an algorithm to compute the inner-outer factorization for a rational transfer function. Finally, we will describe a state space method to compute the Douglas-Shapiro-Shields factorization for a rational function.