<abstract xmlns="http://www.w3.org/1999/xhtml"><p>A complex polynomial is called a Hurwitz polynomial, if all its roots have a real part smaller than zero. This kind of polynomial plays an all-dominant role in stability checks of electrical (analog or digital) networks. In this article we prove that a polynomial p can be shown to be Hurwitz by checking whether the rational function e(p)/o(p) can be realized as a reactance of one port, that is as an electrical impedance or admittance consisting of inductors and capacitors. Here e(p) and o(p) denote the even and the odd part of p [25].</p></abstract>

A complex polynomial is called a Hurwitz polynomial, if all its roots have a real part smaller than zero. This kind of polynomial plays an all-dominant role in stability checks of electrical (analog or digital) networks. In this article we prove that a polynomial p can be shown to be Hurwitz by checking whether the rational function e(p)/o(p) can be realized as a reactance of one port, that is as an electrical impedance or admittance consisting of inductors and capacitors. Here e(p) and o(p) denote the even and the odd part of p [25].

A Test for the Stability of Networks

Chair of Display Technology University of Stuttgart Allmandring 3b, 70596 Stuttgart, Germany

Institute of Computer Science University of Gdansk Wita Stwosza 57, 80-952 Gdansk, Poland

Formalized Mathematics

{"article-title":"A Test for the Stability of Networks"}

A complex polynomial is called a Hurwitz polynomial, if all its roots have a real part smaller than zero. This kind of polynomial plays an all-dominant role in...

A Test for the Stability of Networks

Published Online: Aug 23, 2013

Page range: 47 - 53

DOI: https://doi.org/10.2478/forma-2013-0005

This content is open access.