Semiconcave Control-Lyapunov Functions and Stabilizing Feedbacks

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 Caratheodory solutions of the closed-loop system under an additional assumption.

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