@MISC{HURWITZ2.MIZ,
  AUTHOR = {Rowi\'{n}ska-Schwarzweller, Agnieszka and Schwarzweller, Christoph},
  TITLE = {A Test for the Stability of Networks},
  SECTION1 = {Preliminaries},
  SECTION2 = {Even and Odd Part of Polynomials},
  SECTION3 = {Even and Odd Polynomials and Rational Functions},
  SECTION4 = {Real Positive Polynomials and Rational Functions},
  SECTION5 = {The Theorem},
  DAY = {17},
  MONTH = {January},
  YEAR = {2013},
  ADDRESS1 = {Chair of Display Technology, University of Stuttgart,
              Allmandring 3b, 70596 Stuttgart, Germany},
  ADDRESS2 = {Institute of Computer Science, University of Gdansk,
              Wita Stwosza 57, 80-952 Gdansk, Poland},
  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 (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 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 $p$ \cite{Unb93}.}}

@BOOK{Unb93,
      AUTHOR = {R. Unbehauen},
      TITLE = {Netzwerk- und Filtersynthese: Grundlagen und Anwendungen},
      EDITION = {Fourth},
      PUBLISHER = {Oldenbourg-Verlag},
      YEAR = {1993}}
