Stabilization of a class of bifurcations via state feedback

This paper presents a general method for the control or stabilization of the class of local bifurcations commonly occurring in engineering systems, such as saddle-node, transcritical, pitchfork and Hopf bifurcations. The method presented shows that the problem can be solved by transforming the system into its quadratic normal form, a simplified system with equivalent dynamics, and then examining the resulting dynamics on the center manifold of the system. The dynamics on the center manifold can then be altered by linear and quadratic state feedback of the center states. The feedback gains required are given by simple algebraic combinations of the coefficients of the quadratic normal form