{"paper":{"title":"Certifying Set Attractivity for Discrete-Time Uncertain Nonlinear Switched Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"An AG-function certifies robust local attractivity for a set in uncertain nonlinear switched systems","cross_cats":["cs.SY"],"primary_cat":"eess.SY","authors_text":"Alejandro Anderson, Esteban A. Hernandez-Vargas, Giulia Giordano","submitted_at":"2025-11-17T21:00:19Z","abstract_excerpt":"We introduce a new class of functions, called Attractivity Guarantee (AG)-functions, to certify the attractivity of sets for uncertain nonlinear switched systems in discrete time. The existence of an AG-function associated with a set guarantees the robust local attractivity of that set under the system dynamics. We propose a constructive method for obtaining piecewise-continuous AG-functions based on contractive sets for the system, and show that the existence of a robust control contractive set for the dynamics implies the existence of an appropriate AG-function, and hence the robust local at"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The existence of an AG-function associated with a set guarantees the robust local attractivity of that set under the system dynamics. We propose a constructive method for obtaining piecewise-continuous AG-functions based on contractive sets for the system, and show that the existence of a robust control contractive set for the dynamics implies the existence of an appropriate AG-function.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the existence of a robust control contractive set for the dynamics implies the existence of an appropriate AG-function (and hence robust local attractivity), which is stated as a key implication but without full proof details in the abstract.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"AG-functions certify the robust local attractivity of sets for uncertain nonlinear switched discrete-time systems, constructed from contractive sets.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"An AG-function certifies robust local attractivity for a set in uncertain nonlinear switched systems","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"e0e904a6a3ea21cba578ec2291870df759680be93f14d777d057184e9deb492c"},"source":{"id":"2511.13906","kind":"arxiv","version":2},"verdict":{"id":"3a098bc4-d648-44bb-9de6-51177ef74f52","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-17T20:16:45.742291Z","strongest_claim":"The existence of an AG-function associated with a set guarantees the robust local attractivity of that set under the system dynamics. We propose a constructive method for obtaining piecewise-continuous AG-functions based on contractive sets for the system, and show that the existence of a robust control contractive set for the dynamics implies the existence of an appropriate AG-function.","one_line_summary":"AG-functions certify the robust local attractivity of sets for uncertain nonlinear switched discrete-time systems, constructed from contractive sets.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the existence of a robust control contractive set for the dynamics implies the existence of an appropriate AG-function (and hence robust local attractivity), which is stated as a key implication but without full proof details in the abstract.","pith_extraction_headline":"An AG-function certifies robust local attractivity for a set in uncertain nonlinear switched systems"},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.13906/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":3,"sample":[{"doi":"","year":2024,"title":"Anderson, A., Ohemeng, M., Gonzalez, A., and Hernandez-Vargas, E. (2024). Stabilizability of uncertain switched systems to characterize antibiotic resistance evolution. InIEEE Conference on Decision a","work_id":"c69c6851-fb49-4c98-91b3-a95a604dcd15","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2014,"title":",1500.C.The RCCS Ω 0 is shown along with a zoom into the first controllable sets, confirming the expected inclusion Ck−1(Ω)⊆int Ck(Ω)","work_id":"997f7cd4-039f-4c78-8fb5-4d81987598d8","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Liberzon, D. and Morse, A.S. (2024). Basic problems in stability and design of switched systems.IEEE Control Systems, 44(5), 12–14. Lin, H. and Antsaklis, P.J. (2009). Stability and stabiliz- ability ","work_id":"c5581bae-f8d0-45ca-ae87-e1e04d865289","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":3,"snapshot_sha256":"1ba463aaf7b612030446dc6110775eb123246c19682d76d5d724079516d8a405","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"e781bcd5d8c3a79cab65ef82dfcf32f297ff50e0baeb7741192f3427345274cf"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}