English

Composition of rational functions: state-space realization and applications

Complex Variables 2018-07-06 v1

Abstract

We define two versions of compositions of matrix-valued rational functions of appropriate sizes and whenever analytic at infinity, offer a set of formulas for the corresponding state-space realization, in terms of the realizations of the original functions. Focusing on positive real functions, the first composition is applied to electrical circuits theory along with introducing a connection to networks of feedback loops. The second composition is applied to Stieltjes functions.

Keywords

Cite

@article{arxiv.1807.01753,
  title  = {Composition of rational functions: state-space realization and applications},
  author = {Daniel Alpay and Izchak Lewkowicz},
  journal= {arXiv preprint arXiv:1807.01753},
  year   = {2018}
}
R2 v1 2026-06-23T02:51:09.307Z