# A Test for the Stability of Networks

Agnieszka Rowinska-Schwarzweller; Christoph Schwarzweller

Formalized Mathematics (2013)

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

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topAgnieszka 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 -

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