Local robustness of Hopf bifurcation stabilization

Authors:
Tiebao Yang;Xiang Chen
Affiliations:
Department of Electrical and Computer Engineering, University of Windsor, Windsor, ON, Canada;Department of Electrical and Computer Engineering, University of Windsor, Windsor, ON, Canada
Venue:
IEEE Transactions on Circuits and Systems II: Express Briefs
Year:
2009

Citing 4
Cited 0

Local feedback stabilization and bifurcation control, I. Hopf bifurcation

Systems & Control Letters
Bifurcation Stabilization with Local Output Feedback

SIAM Journal on Control and Optimization
Bifurcation Control via State Feedback for Systems with a Single Uncontrollable Mode

SIAM Journal on Control and Optimization
Brief paper: Local L2 gain of bifurcation stabilization

Automatica (Journal of IFAC)

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Abstract

Local robust analysis via L2 gain method is presented for a class of Hopf bifurcation stabilizing controllers. In particular, we first construct a family of Lyapunov functions for the corresponding critical system, then derive a sufficient condition to compute the L2 gain by solving the Hamilton-Jacobi-Bellman (HJB) inequalities. Local robust analysis can be conducted through computing the local L2 gain achieved by the stabilizing controllers at the critical situation. The theoretical results obtained in this brief provide useful guidance for selecting a robust controller from a given class of stabilizing controllers under Hopf bifurcation. As an example, application to a modified Van der Pol oscillator is discussed in details.