Polynomial stabilization of some control systems by smooth feedbacks

In this article we are interested in polynomial stability for dynamical systems. Sufficient Lyapunov condition is given and the example of double integrator on R
ⁿ
is solved by using two strategies: In the first one we use the backstepping techniques, while in the second we use homogeneous feedback laws with positive degree. As application, the problem of robot manipulators is considered.