Asymptote angles of polynomic root loci

Journal ar
  • Volumen: 71
  • Fecha: 01 September 2016
  • Páginas: 314-317
  • ISSN: 00051098
  • Source Type: Journal
  • DOI: 10.1016/j.automatica.2016.05.025
  • Document Type: Article
  • Publisher: Elsevier Ltd
© 2016 Elsevier Ltd. All rights reserved. In recent publications the plotting rules of polynomially parameterized root loci have been developed for characteristic polynomials in the gain as unknown with degrees 2 and 3. Unfortunately the proof of the asymptote rule is very long and intricate. In this note a generalization of the rule of asymptote angles is addressed for any polynomial with arbitrary degree. Additionally, a simple and shorter proof of the asymptote angles is obtained through the continuous dependence of the roots of the complex characteristic polynomial with respect to a parameter. The geometry of the roots of this polynomial is investigated via a variant of Rouché's theorem.

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