Bifurcation stabilization for nonlinear systems with double-zero eigenvalues

This paper addresses local stabilization for nonlinear systems with static bifurcation. In particular, nonlinear systems are considered where their linearized systems possess double eigenvalues which vanish at the critical point on the equilibrium surface. Conditions are developed for bifurcation stabilization of both the zero equilibrium solution and the post-critical non zero bifurcated equilibrium solution. These conditions can be used to synthesize a local feedback control law