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.
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}
}