Global stabilizability of homogeneous vector fields of odd degree (Q1108248)

The authors study control systems of type \(\dot x=f(x)+Bu\) with f a homogeneous polynomial. They prove a sufficient condition for global stabilizability of the system by a homogeneous polynomial feedback of the same degree as f. The condition is shown to be also necessary for linear systems and implied by a local controllability condition in a particular case. The constructions are based on the Lyapunov function method.