{"id":"https://openalex.org/W2102338235","doi":"https://doi.org/10.1109/cdc.2005.1583263","title":"On the PE stabilization of time-varying systems: open questions and preliminary answers","display_name":"On the PE stabilization of time-varying systems: open questions and preliminary answers","publication_year":2006,"publication_date":"2006-10-04","ids":{"openalex":"https://openalex.org/W2102338235","doi":"https://doi.org/10.1109/cdc.2005.1583263","mag":"2102338235"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2005.1583263","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2005.1583263","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 44th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},"type":"conference-paper","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/A5090052067","display_name":"Antonio Lor\u0131\u0301a","orcid":"https://orcid.org/0000-0003-4223-9397"},"institutions":[{"id":"https://openalex.org/I102475099","display_name":"Sup\u00e9lec","ror":"https://ror.org/00n7gwn90","country_code":"FR","type":"education","lineage":["https://openalex.org/I102475099"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"A. Loria","raw_affiliation_strings":["CNRS-LSS-SUPELEC, Gif-sur-Yvette, France","CNRS-LSS, Sup\u00e9lec, 3, Rue Joliot Curie, 91192 Gif s/Yvette, France. E-mail: loria@lss.supelec.fr"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS-LSS-SUPELEC, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I102475099","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CNRS-LSS, Sup\u00e9lec, 3, Rue Joliot Curie, 91192 Gif s/Yvette, France. E-mail: loria@lss.supelec.fr","institution_ids":["https://openalex.org/I102475099","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058680776","display_name":"Antoine Chaillet","orcid":"https://orcid.org/0000-0003-4095-0468"},"institutions":[{"id":"https://openalex.org/I102475099","display_name":"Sup\u00e9lec","ror":"https://ror.org/00n7gwn90","country_code":"FR","type":"education","lineage":["https://openalex.org/I102475099"]},{"id":"https://openalex.org/I4210097418","display_name":"Laboratoire des signaux et syst\u00e8mes","ror":"https://ror.org/00skw9v43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"A. Chaillet","raw_affiliation_strings":["LSS, Sup\u00e9lec, Gif-sur-Yvette, France","Laboratoire des signaux et syst\u00e8mes"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LSS, Sup\u00e9lec, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I102475099"]},{"raw_affiliation_string":"Laboratoire des signaux et syst\u00e8mes","institution_ids":["https://openalex.org/I4210097418"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065181808","display_name":"Gildas Besan\u00e7on","orcid":"https://orcid.org/0000-0001-5701-6255"},"institutions":[{"id":"https://openalex.org/I4210116740","display_name":"Laboratoire d'Informatique et d'Automatique pour les Syst\u00e8mes","ror":"https://ror.org/02b5vq778","country_code":"FR","type":"facility","lineage":["https://openalex.org/I32881790","https://openalex.org/I4210116740"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"G. Besancon","raw_affiliation_strings":["LAG-ENSIEG, Saint Martin d'Heres, France","Laboratoire d'automatique de Grenoble"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LAG-ENSIEG, Saint Martin d'Heres, France","institution_ids":[]},{"raw_affiliation_string":"Laboratoire d'automatique de Grenoble","institution_ids":["https://openalex.org/I4210116740"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000279658","display_name":"Yacine Chitour","orcid":"https://orcid.org/0000-0002-3214-5824"},"institutions":[{"id":"https://openalex.org/I197681013","display_name":"Universit\u00e9 Paris-Est Cr\u00e9teil","ror":"https://ror.org/05ggc9x40","country_code":"FR","type":"education","lineage":["https://openalex.org/I197681013"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I4210097418","display_name":"Laboratoire des signaux et syst\u00e8mes","ror":"https://ror.org/00skw9v43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Y. Chitour","raw_affiliation_strings":["Universit\u00e9 Paris XII, Orsay, France","Laboratoire des signaux et syst\u00e8mes"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris XII, Orsay, France","institution_ids":["https://openalex.org/I197681013","https://openalex.org/I204730241"]},{"raw_affiliation_string":"Laboratoire des signaux et syst\u00e8mes","institution_ids":["https://openalex.org/I4210097418"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"6847","last_page":"6852"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.9988999962806702,"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":0.9966999888420105,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9958999752998352,"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/backstepping","display_name":"Backstepping","score":0.8783025741577148},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.8131192922592163},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.7652880549430847},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.7209399938583374},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5601776838302612},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5237472057342529},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.5219918489456177},{"id":"https://openalex.org/keywords/double-integrator","display_name":"Double integrator","score":0.49506035447120667},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4703293740749359},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4300987422466278},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.41445326805114746},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.1718403398990631},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1596435308456421},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11126163601875305},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08958074450492859}],"concepts":[{"id":"https://openalex.org/C72218879","wikidata":"https://www.wikidata.org/wiki/Q4839759","display_name":"Backstepping","level":4,"score":0.8783025741577148},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.8131192922592163},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.7652880549430847},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7209399938583374},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5601776838302612},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5237472057342529},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.5219918489456177},{"id":"https://openalex.org/C2779323837","wikidata":"https://www.wikidata.org/wiki/Q5300045","display_name":"Double integrator","level":3,"score":0.49506035447120667},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4703293740749359},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4300987422466278},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.41445326805114746},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.1718403398990631},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1596435308456421},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11126163601875305},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08958074450492859},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2005.1583263","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2005.1583263","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 44th IEEE Conference on Decision and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-00364064v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00364064","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"CDC-ECC 2005 - Joint 44th IEEE Conference on Decision and Control, and European Control Conference, Dec 2005, S\u00e9ville, Spain. ⟨10.1109/cdc.2005.1583263⟩","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1551896781","https://openalex.org/W1560772480","https://openalex.org/W1618010429","https://openalex.org/W1986594128","https://openalex.org/W1993436983","https://openalex.org/W1996293513","https://openalex.org/W2075933120","https://openalex.org/W2090167557","https://openalex.org/W2127988032","https://openalex.org/W2145415070","https://openalex.org/W2147499478","https://openalex.org/W2158302611","https://openalex.org/W6633352224","https://openalex.org/W6683377009"],"related_works":["https://openalex.org/W1963225701","https://openalex.org/W2080488015","https://openalex.org/W3011480163","https://openalex.org/W4402569967","https://openalex.org/W2347533678","https://openalex.org/W4248598780","https://openalex.org/W4244659545","https://openalex.org/W2116395142","https://openalex.org/W2369204337","https://openalex.org/W2507282821"],"abstract_inverted_index":{"We":[0],"address":[1],"the":[2,22,27,30,51,61,66,69,88,94],"following":[3],"question:":[4],"given":[5],"a":[6,10,36,132],"double":[7],"integrator":[8],"and":[9,45,63,84,126],"linear":[11],"control":[12,24,31],"that":[13,29,58,118],"stabilizes":[14],"it":[15,18],"exponentially,":[16],"is":[17,33,80,111],"possible":[19],"to":[20],"use":[21],"same":[23,52,70],"input":[25,32,56,104],"in":[26,87,123,141],"case":[28],"multiplied":[34],"by":[35],"time-varying":[37,124],"term?":[38],"Such":[39],"question":[40],"has":[41,85],"many":[42],"interesting":[43],"motivations":[44],"generalizations:":[46],"1)":[47],"we":[48,113,119],"can":[49],"pose":[50],"problem":[53],"for":[54,100,131],"an":[55],"gain":[57],"depends":[59],"on":[60],"state":[62],"time;":[64],"2)":[65],"stabilization":[67,89,98,125],"\u2013with":[68],"method\u2013of":[71],"chains":[72],"of":[73,75,90,108,143,145],"integrators":[74],"higher":[76],"order":[77],"than":[78],"two":[79],"fundamentally":[81],"more":[82],"complex":[83],"applications":[86],"driftless":[91],"systems;":[92],"3)":[93],"popular":[95],"backstepping":[96],"method":[97,99],"systems":[101],"with":[102],"non-invertible":[103],"terms.":[105],"The":[106],"purpose":[107],"this":[109],"note":[110],"two-fold:":[112],"present":[114,127],"some":[115,128],"open":[116],"questions":[117],"believe":[120],"are":[121,139],"significant":[122],"preliminary":[129],"answers":[130],"simple,":[133],"yet":[134],"challenging":[135],"case-study.":[136],"Our":[137],"solutions":[138],"stated":[140],"terms":[142],"persistency":[144],"excitation.":[146]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}