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Given a locally defined, nondifferentiable but Lipschitz Lyapunov function, we employ it in order to construct a (discontinuous) feedback law which stabilizes the underlying system to any given tolerance. A converse result shows that suitable Lyapunov functions of this type exist under mild assumptions. We also establish that the feedback in question… (More)

A standard finite dimensional nonlinear control system is considered, along with a state constraint set S and a target set Σ. It is proven that open loop S-constrained controllability to Σ implies closed loop S-constrained controllability to the closed δ-neighborhood of Σ, for any specified δ > 0. When the target set Σ satisfies a small time S-constrained… (More)

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