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].
@article{bwmeta1.element.doi-10_2478_forma-2013-0005,
author = {Agnieszka Rowinska-Schwarzweller and Christoph Schwarzweller},
title = {A Test for the Stability of Networks},
journal = {Formalized Mathematics},
volume = {21},
year = {2013},
pages = {47-53},
zbl = {1293.30016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_forma-2013-0005}
}
Agnieszka Rowinska-Schwarzweller; Christoph Schwarzweller. A Test for the Stability of Networks. Formalized Mathematics, Tome 21 (2013) pp. 47-53. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_forma-2013-0005/
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