Asymptote angles of polynomic root loci

• Juan Ignacio Mulero-Martínez ^[1]
  1. [1] Universidad Politécnica de Cartagena

     Universidad Politécnica de Cartagena

     Cartagena, España

     
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 71, 2016, págs. 314-317
• Idioma: inglés
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• Resumen

  • 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.