Resumen de Asymptote angles of polynomic root loci
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.
