Journal of Applied Mathematics
Volume 2011 (2011), Article ID 568048, 21 pages
doi:10.1155/2011/568048
Research Article

An Approach to Robust Control of the Hopf Bifurcation

1Dipartimento di Sistemi e Informatica, Università di Firenze, Via S. Marta 3, 50135 Firenze, Italy
2Dipartimento di Ingegneria dell'Informazione, Università di Siena, Via Roma 56, 53100 Siena, Italy

Received 1 December 2010; Accepted 12 January 2011

Academic Editor: F. Marcellan

Copyright © 2011 Giacomo Innocenti et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The paper illustrates a novel approach to modify the Hopf bifurcation nature via a nonlinear state feedback control, which leaves the equilibrium properties unchanged. This result is achieved by recurring to linear and nonlinear transformations, which lead the system to locally assume the ordinary differential equation representation. Third-order models are considered, since they can be seen as proper representatives of a larger class of systems. The explicit relationship between the control input and the Hopf bifurcation nature is obtained via a frequency approach, that does not need the computation of the center manifold.