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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

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1898-9934
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Volume 14, Issue 4 (Jan 2006)

Issues

Schur's Theorem on the Stability of Networks

Christoph Schwarzweller / Agnieszka Rowińska-Schwarzweller
  • Chair of Display Technology, University of Stuttgart, Allmandring 3b, 70569 Stuttgart, Germany
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2008-06-13 | DOI: https://doi.org/10.2478/v10037-006-0017-9

Schur's Theorem on 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 stability checks of electrical networks.

In this article we prove Schur's criterion [17] that allows to decide whether a polynomial p(x) is Hurwitz without explicitly computing its roots: Schur's recursive algorithm successively constructs polynomials pi(x) of lesser degree by division with x - c, ℜ {c} < 0, such that pi(x) is Hurwitz if and only if p(x) is.

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About the article


Published Online: 2008-06-13

Published in Print: 2006-01-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-006-0017-9.

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