Control of the n-dimensional Takens-Bogdanov bifurcation with applications

Authors:
Francisco A. Carrillo;Fernando Verduzco;Joaquín Delgado
Affiliations:
Hermosillo, Sonora, Mexico and Departamento de Matemáticas, Universidad de Sonora, Sonora, Mexico;Hermosillo, Sonora, Mexico and Departamento de Matemáticas, Universidad de Sonora, Sonora, Mexico;Ciudad de Mexico D.F., Sonora, Mexico and Departamento de Matemáticas, UAM-Iztapalapa, Sonora, Mexico
Venue:
Journal of Dynamical and Control Systems
Year:
2012

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Abstract

An n-dimensional nonlinear control system is considered, whose nominal vector field has a double-zero eigenvalue and no other eigenvalue on the imaginary axis, and then the idea is to find under which conditions there exists a scalar control law such that it is possible to establish a priori, that the closed loop system undergoes the controllable Takens-Bogdanov bifurcation. One application of this result is discussed.