Global Stabilization for Systems Evolving on Manifolds

Details Global Stabilization for Systems Evolving on Manifolds Global Stabilization for Systems Evolving on Manifolds

2004-10-11

arxiv.org/abs/math/0410277v1

Journal of Dynamical and Control Systems, Volume 12, Number 2, pp. 161-184, April 2006

Mathematics

Optimization and Control

25 pages, 0 figues, submitted for publication in October 2004

Scientific paper

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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