@MISC{HURWITZ.MIZ,
  AUTHOR = {Schwarzweller, Christoph and Rowi\'{n}ska-Schwarzweller, Agnieszka},
  TITLE = {Schur's Theorem on the Stability of Networks},
  SECTION1 = {Preliminaries},
  SECTION2 = {More on Polynomials},
  SECTION3 = {Division of Polynomials},
  SECTION4 = {Schur's Theorem},
  DAY = {19},
  MONTH = {October},
  YEAR = {2006},
  ADDRESS1 = {Institute of Computer Science\\University of Gda\'{n}sk\\Wita Stwosza 57, 80-952 Gda\'{n}sk, Poland},
  ADDRESS2 = {Chair of Display Technology\\University of Stuttgart\\Allmandring 3b, 70569 Stuttgart, Germany},
  SUMMARY = {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.\par
   In this article we prove Schur's criterion \cite{SCHUR:1} that
   allows to decide whether a polynomial $p(x)$ is Hurwitz without
   explicitly computing its roots: Schur's recursive algorithm successively
   constructs polynomials $p_i(x)$ of lesser degree by division
   with $x-c$, $\Re\{c\} < 0$, such that $p_i(x)$ is Hurwitz if and only
   if $p(x)$ is.}}

