{"paper":{"title":"Global Stabilization for Systems Evolving on Manifolds","license":"","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Eduardo Sontag, Michael Malisoff, Mikhail Krichman","submitted_at":"2004-10-11T17:51:31Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410277","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}