Asymptotic stabilization of nonlinear affine systems without drift

Issues of asymptotic stabilization of control systems without drift as given by x˙=g(x)u are presented. Conditions on the existence of a smooth time-invariant stabilizer for general nonlinear systems are obtained, specifically, for the case in which the number of inputs is less than that of system states. This is achieved by constructing a Jurdjevic-Quinn type Lyapunov function. Results do not contradict Brockett´s necessary and sufficient condition for the existence of a smooth time-invariant stabilizer. Sufficient conditions for system stabilizability are also attained for both bilinear systems and planar homogeneous systems without drift