DocumentCode :
3535035
Title :
Supercritical Hopf equilibrium points on the boundary of the stability region
Author :
Gouveia, Josaphat R. R. ; Alberto, Luis Fernando C. ; Moraes Amaral, Fabiolo
Author_Institution :
Coll. Math., Fed. Inst. of Bahia, Eunápolis, Brazil
fYear :
2013
fDate :
10-13 Dec. 2013
Firstpage :
5252
Lastpage :
5257
Abstract :
A complete characterization of the boundary of the stability region of nonlinear autonomous dynamical systems is developed admitting the existence of a particular type of non-hyperbolic equilibrium point on the stability boundary, the supercritical Hopf equilibrium points. Under condition of transversality, it is shown that the stability boundary is comprised of all stable manifolds of the hyperbolic equilibrium points lying on the stability boundary union with the center-stable andor center manifolds of the type-k, k ≥ 1, supercritical Hopf equilibrium points on the stability boundary.
Keywords :
nonlinear control systems; stability; nonhyperbolic equilibrium point; nonlinear autonomous dynamical system; stability boundary; supercritical Hopf equilibrium point; transversality condition; Asymptotic stability; Bifurcation; Eigenvalues and eigenfunctions; Manifolds; Power system stability; Stability criteria; Vectors;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on
Conference_Location :
Firenze
ISSN :
0743-1546
Print_ISBN :
978-1-4673-5714-2
Type :
conf
DOI :
10.1109/CDC.2013.6760715
Filename :
6760715
Link To Document :
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