Feedback Stabilization of a class of Nonlinear Systems Using Nonlinear Normal Form

This paper investigates the design of a feedback controller via nonlinear normal form for a class of nonlinear systems. A general second-order nonlinear system affine in control is firstly presented. In general, it is more difficult to construct a nonlinear norm form, since the change of coordinates is achieved by solving the corresponding partial differential equations, which is more troublesome for an abstract nonlinear system. However, for the nonlinear affine system studied in this paper, a change of coordinates is found successfully and used to transform the nonlinear affine system into its nonlinear normal form, based on which the stabilizing state feedback control law and the Lyapunov function are obtained through a constructive design method. Then, this design approach is extended to stabilize nth-order nonlinear systems with a similar structure. Finally, the proposed controller is applied to control the second-order system, and simulation results show that the developed controller can effectively guarantees the stability of the closed loop system.