Mechanical & Industrial Engineering
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 halfplane, 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.
Irofti, Dina Alina; Gu, Keqin; Boussaada, Islam; and Niculescu, Silviu-Iulian, "Some insights into the migration of double imaginary roots under small deviation of two parameters" (2018). SIUE Faculty Research, Scholarship, and Creative Activity. 82.
Acoustics, Dynamics, and Controls Commons, Controls and Control Theory Commons, Control Theory Commons, Dynamic Systems Commons, Navigation, Guidance, Control and Dynamics Commons, Process Control and Systems Commons