The aim of the thesis is to study the stabilization of the system x˙ = f(x)+bu.Here the linearization system contains a high order controllable mode. First, by center manifold theory, we can reduce the dynamics of the given system (higher order system) to the dynamics of the center manifold system(lower order system).Second, using normal forms or Lyapunov function, we can find a sufficient condition such that the center manifold system is locally asymptotically stable. That is,we can control u(x) such that the given system is stabilized.