Stabilization of general nonlinear control systems via center manifold and approximation techniques

This paper considers the stabilization of a class of general nonlinear control systems. Under some mild conditions, a general nonlinear control system can be transformed into a normal form, which is suitable for the center manifold approach. A kind of controller in the polynomial form is proposed to stabilize the systems. First, the type and degree of controllers are chosen to assure the approximation degree of the center manifold. Then the coefficients are chosen to make the dynamics of the center manifold of the closed-loop systems stable. To test the approximate stability of the dynamics on the center manifold, the Lyapunov function with homogeneous derivative proposed in [6] is used.