{"paper":{"title":"Ultimate Boundedness for Switched Systems with Multiple Equilibria Under Disturbances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SY","authors_text":"Ioannis Poulakakis, Sushant Veer","submitted_at":"2018-09-08T03:27:50Z","abstract_excerpt":"In this paper, we investigate the robustness to external disturbances of switched discrete and continuous systems with multiple equilibria. It is shown that if each subsystem of the switched system is Input-to-State Stable (ISS), then under switching signals that satisfy an average dwell-time bound, the solutions are ultimately bounded within a compact set. Furthermore, the size of this set varies monotonically with the supremum norm of the disturbance signal. It is observed that when the subsystems share a common equilibrium, ISS is recovered for solutions of the corresponding switched system"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02750","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"}