  The main goal of this paper is to demonstrate the usefulness of certain ideas
from System Theory in the study of problems from complex analysis. With this
paper, we also aim to encourage analysts, who might not be familiar with System
Theory, colligations or operator models to take a closer look at these topics.
For this reason, we present a short introduction to the necessary background.
The method of system realizations of analytic functions often provides new
insights into and interpretations of results relating to the objects under
consideration. In this paper we will use a well-studied topic from classical
analysis as an example. More precisely, we will look at the classical Schur
algorithm from the perspective of System Theory. We will confine our
considerations to rational inner functions. This will allow us to avoid
questions involving limits and will enable us to concentrate on the algebraic
aspects of the problem at hand. Given a non-negative integer (n), we describe
all system realizations of a given rational inner function of degree (n) in
terms of an appropriately constructed equivalence relation in the set of all
unitary ((n + 1) \times (n + 1) )-matrices. The concept of Redheffer coupling
of colligations gives us the possibility to choose a particular representative
from each equivalence class. The Schur algorithm for a rational inner function
is, consequently, described in terms of the state space representation.

Complex Variables;Spectral Theory