# Schur's Theorem on the Stability of Networks

Christoph Schwarzweller; Agnieszka Rowińska-Schwarzweller

Formalized Mathematics (2006)

- Volume: 14, Issue: 4, page 135-142
- ISSN: 1426-2630

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topChristoph Schwarzweller, and Agnieszka Rowińska-Schwarzweller. "Schur's Theorem on the Stability of Networks." Formalized Mathematics 14.4 (2006): 135-142. <http://eudml.org/doc/267400>.

@article{ChristophSchwarzweller2006,

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 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.},

author = {Christoph Schwarzweller, Agnieszka Rowińska-Schwarzweller},

journal = {Formalized Mathematics},

language = {eng},

number = {4},

pages = {135-142},

title = {Schur's Theorem on the Stability of Networks},

url = {http://eudml.org/doc/267400},

volume = {14},

year = {2006},

}

TY - JOUR

AU - Christoph Schwarzweller

AU - Agnieszka Rowińska-Schwarzweller

TI - Schur's Theorem on the Stability of Networks

JO - Formalized Mathematics

PY - 2006

VL - 14

IS - 4

SP - 135

EP - 142

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 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.

LA - eng

UR - http://eudml.org/doc/267400

ER -

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## Citations in EuDML Documents

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- Hiroyuki Okazaki, Yasunari Shidama, Uniqueness of Factoring an Integer and Multiplicative Group Z/pZ*
- Artur Korniłowicz, Christoph Schwarzweller, The First Isomorphism Theorem and Other Properties of Rings

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