We develop discontinuous controllers for stabilizing n-dimensional nonholonomic mechanical systems given in power form. We show that the stabilization of the whole system turns out to be a simultaneous stabilization of (n-3) driftless subsystems. The control strategy is based on the technique of invariant manifolds. Moreover, it is shown that we could improve the rate of convergence of the state vector by the use of dynamic controllers. A numerical procedure is proposed to filter the noisy measurement without affecting the dynamic of the controller.