Constructive Lyapunov functions and stabilizing feedback for nonlinear systems

This paper deals with the stabilization for a broad class of nonlinear systems. First, we construct smooth Lyapunov functions from a known weak control Lyapunov function of the system. It is proved that a weak control Lyapunov function satisfying a less conservative condition can be used to design a globally stabilizing control law. The simulation shows the effectiveness of the method.