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, and Subbotin (CLSS). We generalize their 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 with respect to actuator errors, under small observation noise.
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2000 Mathematics Subject Classification. 93B05.
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Malisoff, M., Krichman, M. & Sontag, E. Global Stabilization for Systems Evolving on Manifolds. J Dyn Control Syst 12, 161–184 (2006). https://doi.org/10.1007/s10450-006-0379-x
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DOI: https://doi.org/10.1007/s10450-006-0379-x