{"paper":{"title":"Bifurcation of limit cycles from a switched equilibrium in planar switched systems and its application to power converters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Oleg Makarenkov","submitted_at":"2017-12-20T07:59:40Z","abstract_excerpt":"We consider a switched system of two subsystems that are activated as the trajectory enters the regions $\\{(x,y):x>\\bar x\\}$ and $\\{(x,y):x<-\\bar x\\}$ respectively, where $\\bar x$ is a positive parameter. We prove that a regular asymptotically stable equilibrium of the associated Filippov equation of sliding motion (corresponding to $\\bar x=0$) yields an orbitally stable limit cycle for all $\\bar x>0$ sufficiently small. The research is motivated by an application to a dc-dc power converter, where $\\bar x>0$ is used in place of $\\bar x=0$ to avoid sliding motions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07356","kind":"arxiv","version":2},"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"}