<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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.</p><p>In this article we prove Schur's criterion [17] that allows to decide whether a polynomial <italic>p(x)</italic> is Hurwitz without explicitly computing its roots: Schur's recursive algorithm successively constructs polynomials <italic>pi(x)</italic> of lesser degree by division with <italic>x</italic> - <italic>c</italic>, ℜ {c} &lt; 0, such that <italic>pi(x)</italic> is Hurwitz if and only if <italic>p(x)</italic> is.</p></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.

Schur's Theorem on the Stability of Networks

Institute of Computer Science, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

Chair of Display Technology, University of Stuttgart, Allmandring 3b, 70569 Stuttgart, Germany

Formalized Mathematics

{"article-title":"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...

Schur's Theorem on the Stability of Networks

Pubblicato online: 13 giu 2008

Pagine: 135 - 142

DOI: https://doi.org/10.2478/v10037-006-0017-9

This content is open access.