{"id":"https://openalex.org/W2021719412","doi":"https://doi.org/10.1137/s0363012900375342","title":"Semiconcave Control-Lyapunov Functions and Stabilizing Feedbacks","display_name":"Semiconcave Control-Lyapunov Functions and Stabilizing Feedbacks","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2021719412","doi":"https://doi.org/10.1137/s0363012900375342","mag":"2021719412"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012900375342","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012900375342","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-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/A5000713548","display_name":"Ludovic Rifford","orcid":"https://orcid.org/0000-0003-2084-7471"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Lyon 1 Universit\u00e9","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I4210104796","display_name":"Institut Camille Jordan","ror":"https://ror.org/01ekw7f87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Ludovic Rifford","raw_affiliation_strings":["Institut Girard Desargues, Universit\u00e9 Lyon I, 43 Bd du 11 Novembre 1918, 69622 Villeurbanne Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut Girard Desargues, Universit\u00e9 Lyon I, 43 Bd du 11 Novembre 1918, 69622 Villeurbanne Cedex, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I4210104796"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5000713548"],"corresponding_institution_ids":["https://openalex.org/I100532134","https://openalex.org/I4210104796"],"apc_list":null,"apc_paid":null,"fwci":10.2198,"has_fulltext":false,"cited_by_count":107,"citation_normalized_percentile":{"value":0.99041173,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"41","issue":"3","first_page":"659","last_page":"681"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9948999881744385,"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/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.992900013923645,"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/mathematics","display_name":"Mathematics","score":0.818953812122345},{"id":"https://openalex.org/keywords/discontinuity","display_name":"Discontinuity (linguistics)","score":0.7082645893096924},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.6968013644218445},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.6151813268661499},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.5869892835617065},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.570472002029419},{"id":"https://openalex.org/keywords/stability-theory","display_name":"Stability theory","score":0.5546938180923462},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5029248595237732},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.47284916043281555},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4453422725200653},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.43695613741874695},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38834232091903687},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2816128134727478},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22559985518455505},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1535036563873291},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1270655393600464}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.818953812122345},{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.7082645893096924},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6968013644218445},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6151813268661499},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.5869892835617065},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.570472002029419},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.5546938180923462},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5029248595237732},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.47284916043281555},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4453422725200653},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.43695613741874695},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38834232091903687},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2816128134727478},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22559985518455505},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1535036563873291},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1270655393600464},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0363012900375342","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012900375342","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.463.4760","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.463.4760","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.archives-ouvertes.fr/docs/00/76/90/01/PDF/SIAM_RIFFORD_2002.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1516412357","https://openalex.org/W1528336988","https://openalex.org/W1529034024","https://openalex.org/W1547240457","https://openalex.org/W1551360398","https://openalex.org/W1960239420","https://openalex.org/W1971044547","https://openalex.org/W1975739077","https://openalex.org/W1985141482","https://openalex.org/W1986091057","https://openalex.org/W1990328798","https://openalex.org/W1991408703","https://openalex.org/W2007626594","https://openalex.org/W2011070788","https://openalex.org/W2022607740","https://openalex.org/W2032128836","https://openalex.org/W2032316144","https://openalex.org/W2041076275","https://openalex.org/W2041485674","https://openalex.org/W2050439892","https://openalex.org/W2052241257","https://openalex.org/W2057820893","https://openalex.org/W2069769125","https://openalex.org/W2116630766","https://openalex.org/W2140531311","https://openalex.org/W2152112251","https://openalex.org/W2322654430","https://openalex.org/W2415568859","https://openalex.org/W2485990915","https://openalex.org/W4319776160"],"related_works":["https://openalex.org/W1516195074","https://openalex.org/W2019026841","https://openalex.org/W2142014702","https://openalex.org/W2364440354","https://openalex.org/W3134030163","https://openalex.org/W2167699502","https://openalex.org/W2101609760","https://openalex.org/W2071231746","https://openalex.org/W2511534287","https://openalex.org/W2918134800"],"abstract_inverted_index":{"We":[0,12],"study":[1],"the":[2,38,47,60,64],"general":[3],"problem":[4],"of":[5,7,35,40,52,63],"stabilization":[6],"globally":[8],"asymptotically":[9],"controllable":[10],"systems.":[11],"construct":[13],"discontinuous":[14],"feedback":[15],"laws,":[16],"and":[17],"particularly":[18],"we":[19],"make":[20],"it":[21],"possible":[22],"to":[23,56],"choose":[24],"these":[25],"continuous":[26],"outside":[27],"a":[28],"small":[29],"set":[30,51],"(closed":[31],"with":[32],"measure":[33],"zero)":[34],"discontinuity":[36],"in":[37,46],"case":[39],"control":[41],"systems":[42],"which":[43],"are":[44],"affine":[45],"control;":[48],"moreover":[49],"this":[50],"singularities":[53],"is":[54],"shown":[55],"be":[57],"repulsive":[58],"for":[59],"Carath\u00e9odory":[61],"solutions":[62],"closed-loop":[65],"system":[66],"under":[67],"an":[68],"additional":[69],"assumption.":[70]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":8}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}