Some insights into the migration of double imaginary roots under small deviation of two parameters

• Autores: Dina Alina Irofti, Keqing Lu, Islam Boussaada, Silviu-Iulian Niculescu
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 88, 2018, págs. 91-97
• Idioma: inglés
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• Resumen

  • This paper studies the migration of double imaginary roots of the systems’ characteristic equation when two parameters are subjected to small deviations. The proposed approach covers a wide range of models. Under the least degeneracy assumptions, we found that the local stability crossing curve has a cusp at the point that corresponds to the double root, and it divides the neighborhood of this point into an S-sector and a G-sector. When the parameters move into the G-sector, one of the roots moves to the right half-plane, and the other moves to the left half-plane. When the parameters move into the S-sector, both roots move either to the left half-plane or the right half-plane depending on the sign of a quantity that depends on the characteristic function and its derivatives up to the third order.