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.

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