Brief paper: Local L2 gain of bifurcation stabilization
Automatica (Journal of IFAC)
Local robustness of Hopf bifurcation stabilization
IEEE Transactions on Circuits and Systems II: Express Briefs
Control of the n-dimensional Takens-Bogdanov bifurcation with applications
Journal of Dynamical and Control Systems
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The state feedback control of bifurcations with quadratic or cubic degeneracy is addressed for systems with a single uncontrollable mode. Based on normal forms and invariants, the classification of bifurcations for systems with a single uncontrollable mode is obtained (Table 1). Using invariants, stability characterizations are derived for a family of bifurcations, including saddle-node bifurcations, transcritical bifurcations, pitchfork bifurcations, and bifurcations with a cusp or hysteresis phenomenon. Bifurcations in systems under perturbed feedbacks are also addressed. In the case of a saddle-node bifurcation, continuous but not differentiable feedbacks are introduced to locally remove the bifurcation and to achieve the stability.