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Global Stabilization for Systems Evolving on Manifolds

Michael Malisoff·Mikhail Krichman·Eduardo Sontag
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Abstract

We show that any globally asymptotically controllable system on any smooth manifold can be globally stabilized by a state feedback. Since we allow discontinuous feedbacks, we interpret the solutions of our systems in the ``sample and hold'' sense introduced by Clarke-Ledyaev-Sontag-Subbotin (CLSS). Our work generalizes the CLSS Theorem which is the special case of our result for systems on Euclidean space. We apply our result to the input-to-state stabilization of systems on manifolds relative to actuator errors, under small observation noise.

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Michael Malisoff, Mikhail Krichman, Eduardo Sontag. 2004-10-11. Global Stabilization for Systems Evolving on Manifolds. https://arxiv.org/abs/math/0410277

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