We consider parameter-dependent dynamical systems, controlled by a smooth nonlinear state feedback, when the uncontrolled system undergoes a bifurcation. We try to design the feedback in such a way that when the parameter is slowly moved through the bifurcation point, there is an immediate exchange of stability, that is, the state follows a prescribed stable equilibrium branch created in the bifurcation.
This work was done at the Weierstrass Institute in Berlin, and supported by the Nonlinear Control Network of the European Community. An overview is given in this proceedings, and the main result on dynamic Hopf bifurcations is described here.