{"paper":{"title":"High-order S-Lemma with application to stability of a class of switched nonlinear systems","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Fuchun Sun, Kuize Zhang, Lijun Zhang","submitted_at":"2014-03-05T06:43:19Z","abstract_excerpt":"This paper extends some results on the S-Lemma proposed by Yakubovich and uses the improved results to investigate the asymptotic stability of a class of switched nonlinear systems.\n  Firstly, the strict S-Lemma is extended from quadratic forms to homogeneous functions with respect to any dilation, where the improved S-Lemma is named the strict homogeneous S-Lemma (the SHS-Lemma for short). In detail, this paper indicates that the strict S-Lemma does not necessarily hold for homogeneous functions that are not quadratic forms, and proposes a necessary and sufficient condition under which the SH"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1016","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"}