{"id":"https://openalex.org/W4391020211","doi":"https://doi.org/10.1109/cdc49753.2023.10383373","title":"A Recurrence-Based Direct Method for Stability Analysis and GPU-Based Verification of Non-Monotonic Lyapunov Functions","display_name":"A Recurrence-Based Direct Method for Stability Analysis and GPU-Based Verification of Non-Monotonic Lyapunov Functions","publication_year":2023,"publication_date":"2023-12-13","ids":{"openalex":"https://openalex.org/W4391020211","doi":"https://doi.org/10.1109/cdc49753.2023.10383373"},"language":"en","primary_location":{"id":"doi:10.1109/cdc49753.2023.10383373","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc49753.2023.10383373","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022106692","display_name":"Roy Siegelmann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Roy Siegelmann","raw_affiliation_strings":["Department of Applied Mathematics and Statistics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Statistics","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090011683","display_name":"Yue Shen","orcid":"https://orcid.org/0000-0002-2985-825X"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yue Shen","raw_affiliation_strings":["Johns Hop-kins University,Department of Electrical and Computer Engineering,Baltimore,MD,USA,21218"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johns Hop-kins University,Department of Electrical and Computer Engineering,Baltimore,MD,USA,21218","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072319687","display_name":"Fernando Paganini","orcid":"https://orcid.org/0000-0002-1258-9049"},"institutions":[{"id":"https://openalex.org/I4210147939","display_name":"Universidad ORT Uruguay","ror":"https://ror.org/03ypykr22","country_code":"UY","type":"education","lineage":["https://openalex.org/I4210147939"]}],"countries":["UY"],"is_corresponding":false,"raw_author_name":"Fernando Paganini","raw_affiliation_strings":["Universidad ORT Uruguay,Montevideo","Universidad ORT Uruguay, Montevideo"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad ORT Uruguay,Montevideo","institution_ids":["https://openalex.org/I4210147939"]},{"raw_affiliation_string":"Universidad ORT Uruguay, Montevideo","institution_ids":["https://openalex.org/I4210147939"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032910355","display_name":"Enrique Mallada","orcid":"https://orcid.org/0000-0003-1568-1833"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Enrique Mallada","raw_affiliation_strings":["Johns Hop-kins University,Department of Electrical and Computer Engineering,Baltimore,MD,USA,21218"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johns Hop-kins University,Department of Electrical and Computer Engineering,Baltimore,MD,USA,21218","institution_ids":["https://openalex.org/I145311948"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7766,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.70583362,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"6665","last_page":"6672"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.7468156218528748},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.6512218713760376},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5595827102661133},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5111809372901917},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4983334541320801},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4429478049278259},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3769272565841675},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3328275680541992},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3251502513885498},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3208048939704895},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14884406328201294},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.14508411288261414},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1417638659477234},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.1363356113433838},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09413334727287292}],"concepts":[{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.7468156218528748},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6512218713760376},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5595827102661133},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5111809372901917},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4983334541320801},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4429478049278259},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3769272565841675},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3328275680541992},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3251502513885498},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3208048939704895},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14884406328201294},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.14508411288261414},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1417638659477234},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.1363356113433838},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09413334727287292},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc49753.2023.10383373","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc49753.2023.10383373","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4486440670","display_name":null,"funder_award_id":"CAREER 1752362,CPS 2136324","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W238693918","https://openalex.org/W374079423","https://openalex.org/W1496537269","https://openalex.org/W1966397236","https://openalex.org/W1969598406","https://openalex.org/W2000245888","https://openalex.org/W2009668633","https://openalex.org/W2021313930","https://openalex.org/W2086448962","https://openalex.org/W2104575444","https://openalex.org/W2115520718","https://openalex.org/W2119807669","https://openalex.org/W2153943247","https://openalex.org/W2155689575","https://openalex.org/W2249585788","https://openalex.org/W2314410691","https://openalex.org/W2964117770","https://openalex.org/W2964239200","https://openalex.org/W4307309484","https://openalex.org/W4315472354","https://openalex.org/W6846295675"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2077314575","https://openalex.org/W4315701745","https://openalex.org/W1990290471","https://openalex.org/W4380682190","https://openalex.org/W2005710836","https://openalex.org/W2102386043","https://openalex.org/W2945307361","https://openalex.org/W2116636209","https://openalex.org/W2053698688"],"abstract_inverted_index":{"Lyapunov's":[0],"direct":[1,123],"method":[2,30,81,124],"is":[3,31,58,76,140,176],"a":[4,9,35,55,122,197],"powerful":[5],"tool":[6],"that":[7,24,79,125,148],"provides":[8],"rigorous":[10],"framework":[11],"for":[12,18],"stability":[13,180,190],"analysis":[14],"and":[15,61,105,181,191],"control":[16],"design":[17],"dynamical":[19,51],"systems.":[20],"A":[21,138],"critical":[22],"step":[23],"enables":[25],"the":[26,29,32,47,50,71,77,80,98,106,109,127,132,151,167,183,217],"application":[27],"of":[28,34,49,73,86,100,108,129,136,169,216],"existence":[33],"Lyapunov":[36,56],"function":[37,41,57],"<tex":[38,87,101,141,157,172,203],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[39,88,102,142,158,173,204],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$V-\\mathrm{a}$</tex>":[40],"whose":[42],"value":[43],"monotonically":[44],"decreases":[45],"along":[46],"trajectories":[48,107],"system.":[52,110],"Unfortunately,":[53],"finding":[54],"often":[59],"tricky":[60],"requires":[62,82],"ingenuity,":[63],"domain":[64],"knowledge,":[65],"or":[66],"significant":[67],"computational":[68],"power.":[69],"At":[70],"core":[72],"this":[74,112,118],"challenge":[75],"fact":[78],"every":[83,146],"sub-level":[84,170],"set":[85,139,152],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$V(V_{\\leq":[89],"c})$</tex>":[90],"to":[91,116,154,178,187,200,211],"be":[92],"forward":[93],"invariant,":[94],"thus":[95],"implicitly":[96],"coupling":[97],"geometry":[99],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$V_{\\leq":[103,174],"c}$</tex>":[104,175],"In":[111],"paper,":[113],"we":[114],"seek":[115],"disentangle":[117],"dependence":[119],"by":[120],"developing":[121],"substitutes":[126],"concept":[128],"invariance":[130],"with":[131],"more":[133],"flexible":[134],"notion":[135],"recurrence.":[137],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$(\\tau-)$</tex>":[143],"recurrent":[144],"if":[145],"trajectory":[147],"starts":[149],"in":[150],"returns":[153],"it":[155],"(within":[156],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\tau$</tex>":[159],"seconds).":[160],"We":[161,194],"show":[162],"that,":[163],"under":[164],"mild":[165],"conditions,":[166],"recurrence":[168,208],"sets":[171],"sufficient":[177],"guarantee":[179],"introduce":[182],"appropriate":[184],"stronger":[185],"notions":[186],"obtain":[188],"asymptotic":[189],"exponential":[192],"stability.":[193],"further":[195],"provide":[196],"GPU-based":[198],"algorithm":[199],"verify":[201],"whether":[202],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$V$</tex>":[205],"satisfies":[206],"such":[207],"conditions":[209],"up":[210],"an":[212],"arbitrarily":[213],"small":[214],"neighborhood":[215],"equilibrium.":[218]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}