We study the general problem of stabilization of globally asymptotically controllable systems. We construct discontinuous feedback laws, and particularly we make it possible to choose these continuous outside a small set (closed with measure zero) of discontinuity in the case of control systems which are affine in the control; moreover this set of singularities is shown to be repulsive for the Carathéodory solutions of the closed-loop system under an additional assumption.
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Ludovic Rifford (2002) studied this question.
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