Linearized Control Systems and Applications to Smooth Stabilization

For a control system $\dot x = f(x,u)$, the author proves that, for generic feedback laws u such that $f(x,u(x))$ does not vanish, the linearized control systems around the trajectories of $\dot x = f(x,u(x))$ have the same strong accessibility algebra as f. Applications are given to the smooth stabilization problem.