{"paper":{"title":"Necessary condition on Lyapunov functions corresponding to the globally asymptotically stable equilibrium point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Chirayu D. Athalye, Debasattam Pal, Harish K. Pillai","submitted_at":"2014-05-04T21:41:47Z","abstract_excerpt":"It is well known that, the existence of a Lyapunov function is a sufficient condition for stability, asymptotic stability, or global asymptotic stability of an equilibrium point of an autonomous system $\\dot{\\mathbf{x}} = f(\\mathbf{x})$. In variants of Lyapunov theorems, the condition for a Lyapunov candidate $V$ (continuously differentiable and positive definite function) to be a Lyapunov function is that its time derivative along system trajectories must be negative semi-definite or negative definite. Numerically checking positive definiteness of $V$ is very difficult; checking negative defi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0747","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"}