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Remarks on control Lyapunov functions for discontinuous stabilizing feedback
Proceedings of 32nd IEEE Conference on Decision and Control
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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.
doi:10.1109/cdc.1993.325127
fatcat:7vyltkcnrrdvrf25ql52d3viya