# A Test for the Stability of Networks

Formalized Mathematics (2013)

• Volume: 21, Issue: 1, page 47-53
• ISSN: 1426-2630

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## Abstract

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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].

## How to cite

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Agnieszka Rowinska-Schwarzweller, and Christoph Schwarzweller. "A Test for the Stability of Networks." Formalized Mathematics 21.1 (2013): 47-53. <http://eudml.org/doc/267528>.

@article{AgnieszkaRowinska2013,
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].},
author = {Agnieszka Rowinska-Schwarzweller, Christoph Schwarzweller},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {47-53},
title = {A Test for the Stability of Networks},
url = {http://eudml.org/doc/267528},
volume = {21},
year = {2013},
}

TY - JOUR
AU - Agnieszka Rowinska-Schwarzweller
AU - Christoph Schwarzweller
TI - A Test for the Stability of Networks
JO - Formalized Mathematics
PY - 2013
VL - 21
IS - 1
SP - 47
EP - 53
AB - 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].
LA - eng
UR - http://eudml.org/doc/267528
ER -

## References

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