Nonlinear feedback controller in the phase plane: Design of N-order nonlinear system and its performance

This paper is concerned with nonlinear feedback controller design which based on the phase plane behavior. The controller is to minimize the difference between nonlinear closed-loop vector fields and stabilized closed-loop vector fields. We obtain the stabilized closed-loop vector fields by taking a first order Taylor series approximation to linearize the original nonlinear system. The globally asymptotically stabilization of the controller is also guaranteed by considering the Lyapunov function on the phase plane. The effectiveness of the proposed controller is shown by simulation.