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

Dina Irofti 1 Keqin Gu 2 Islam Boussaada 1 Silviu-Iulian Niculescu 3, 1
3 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : 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.
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Automatica, Elsevier, 2018, 88, pp.91-97. 〈10.1016/j.automatica.2017.11.015〉
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Dina Irofti, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu. Some insights into the migration of double imaginary roots under small deviation of two parameters. Automatica, Elsevier, 2018, 88, pp.91-97. 〈10.1016/j.automatica.2017.11.015〉. 〈hal-01712829〉

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