Stabilization of feedforward systems approximated by a non-linear chain of integrators

We prove that, for any odd integer p and any strictly positive integer n, feedforward systems which are approximated at the origin by a chain of integrators of degree p and length n can be globally asymptotically stabilized by bounded smooth time-invariant state feedbacks. Our proof is based on the construction of a Lyapunov function and the feedback laws we obtain are given by explicit formulas.

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