Robust stability at the Swallowtail singularity

Kirillov, Oleg and Overton, Michael (2013) Robust stability at the Swallowtail singularity. Frontiers in Physics, 1. ISSN 2296-424X

Text (Article)
2013frontiersphysics.pdf - Published Version
Available under License Creative Commons Attribution.

Download (3MB) | Preview
Official URL:


Consider the set of monic fourth-order real polynomials transformed so that the constant term is one. In the three-dimensional space of the coefficients describing this set, the domain of asymptotic stability is bounded by a surface with the Whitney umbrella singularity. The maximum of the real parts of the roots of these polynomials is globally minimized at the Swallowtail singular point of the discriminant surface of the set corresponding to a negative real root of multiplicity four. Motivated by this example, we review recent works on robust stability, abscissa optimization, heavily damped systems, dissipation-induced instabilities, and eigenvalue dynamics in order to point out some connections that appear to be not widely known.

Item Type: Article
Uncontrolled Keywords: abscissa, optimization, overdamping, asymptotic stability, Whitney umbrella, Swallowtail, caustic, eigenvalue dynamics
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Oleg Kirillov
Date Deposited: 10 Jan 2017 11:14
Last Modified: 01 Aug 2021 01:32

Actions (login required)

View Item View Item


Downloads per month over past year

View more statistics