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It is proven that, if, for any positive time T, there exists an open-loop control $u (a,t)$ depending continuously on the initial data a, vanishing for $a = 0$, and steering a small neighborhood of 0 into 0 in time T, then the control system can be locally stabilized in small time by means of continuous time-varying feedback law, provided that the dimension of the state space is at least 4 and the strong accessibility rank condition holds.
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Jean‐Michel Coron (1995) studied this question.
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