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Local Robustness of Hopf Bifurcation Stabilization

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2 Author(s)
Tiebao Yang ; Dept. of Electr. & Comput. Eng., Univ. of Windsor, Windsor, ON ; Xiang Chen

Local robust analysis via L 2 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 L 2 gain by solving the Hamilton-Jacobi-Bellman (HJB) inequalities. Local robust analysis can be conducted through computing the local L 2 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.

Published in:

Circuits and Systems II: Express Briefs, IEEE Transactions on  (Volume:56 ,  Issue: 1 )

Date of Publication:

Jan. 2009

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