Remarks on control Lyapunov functions for discontinuous stabilizing feedback

Abstract
We present a formula for a stabilizing feedback law under the assumption that a piecewise smooth control-Lyapunov function exists. The resulting feedback is continuous at the origin and smooth everywhere except on a hypersurface of codimension 1. We provide an explicit and 'universal' formula. Finally, we mention a general result connecting asymptotic controllability and the existence of control-Lyapunov functions in the sense of nonsmooth optimization.

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