{"id":"https://openalex.org/W2109966077","doi":"https://doi.org/10.1109/tac.2011.2157405","title":"Extended Lie Brackets for Nonlinear Time-Delay Systems","display_name":"Extended Lie Brackets for Nonlinear Time-Delay Systems","publication_year":2011,"publication_date":"2011-05-25","ids":{"openalex":"https://openalex.org/W2109966077","doi":"https://doi.org/10.1109/tac.2011.2157405","mag":"2109966077"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2011.2157405","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2011.2157405","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00625401","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079337546","display_name":"Claudia Califano","orcid":"https://orcid.org/0000-0001-5377-1798"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Claudia Califano","raw_affiliation_strings":["Dipartimento di Information e Sistemistica Antonio Ruberti, Universit\u00e0 di Roma La Sapienza, Rome, Italy","Dip. di Inform. e Sist. \u201cAntonio Ruberti\u201d, Univ. di Roma \u201cLa Sapienza\u201d, Rome, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Information e Sistemistica Antonio Ruberti, Universit\u00e0 di Roma La Sapienza, Rome, Italy","institution_ids":["https://openalex.org/I861853513"]},{"raw_affiliation_string":"Dip. di Inform. e Sist. \u201cAntonio Ruberti\u201d, Univ. di Roma \u201cLa Sapienza\u201d, Rome, Italy","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085487632","display_name":"Luis Alejandro M\u00e1rquez\u2013Mart\u00ednez","orcid":"https://orcid.org/0000-0002-0364-3808"},"institutions":[{"id":"https://openalex.org/I64663401","display_name":"Centro de Investigaci\u00f3n Cient\u00edfica y de Educaci\u00f3n Superior de Ensenada","ror":"https://ror.org/04znhwb73","country_code":"MX","type":"facility","lineage":["https://openalex.org/I64663401"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Luis Alejandro Marquez-Martinez","raw_affiliation_strings":["CICESE, Ensenada, Mexico","CICESE Research Center, Ensenada, Mexico"],"affiliations":[{"raw_affiliation_string":"CICESE, Ensenada, Mexico","institution_ids":["https://openalex.org/I64663401"]},{"raw_affiliation_string":"CICESE Research Center, Ensenada, Mexico","institution_ids":["https://openalex.org/I64663401"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030112128","display_name":"Claude H. Moog","orcid":"https://orcid.org/0000-0003-3803-8760"},"institutions":[{"id":"https://openalex.org/I4210117005","display_name":"Laboratoire des Sciences du Num\u00e9rique de Nantes","ror":"https://ror.org/02snf8m58","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100445878","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I205703379","https://openalex.org/I4210117005","https://openalex.org/I4210124215","https://openalex.org/I4210127572","https://openalex.org/I4210139971","https://openalex.org/I97188460","https://openalex.org/I97188460"]},{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]}],"countries":["FR","MX"],"is_corresponding":false,"raw_author_name":"Claude H. Moog","raw_affiliation_strings":["LUNAM, IRCCyN, UMR, C.N.R.S., Nantes, France","IRCCyN, UNAM, Nantes, France"],"affiliations":[{"raw_affiliation_string":"LUNAM, IRCCyN, UMR, C.N.R.S., Nantes, France","institution_ids":["https://openalex.org/I4210117005"]},{"raw_affiliation_string":"IRCCyN, UNAM, Nantes, France","institution_ids":["https://openalex.org/I8961855"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5079337546"],"corresponding_institution_ids":["https://openalex.org/I861853513"],"apc_list":null,"apc_paid":null,"fwci":7.879,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.97170639,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"56","issue":"9","first_page":"2213","last_page":"2218"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9972000122070312,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9972000122070312,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9940000176429749,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9940000176429749,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5118919610977173},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.42267173528671265},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4048033654689789},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3955550193786621},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3742440342903137},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33545777201652527},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32629114389419556},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3215213716030121},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10166433453559875},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09433075785636902}],"concepts":[{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5118919610977173},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.42267173528671265},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4048033654689789},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3955550193786621},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3742440342903137},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33545777201652527},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32629114389419556},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3215213716030121},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10166433453559875},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09433075785636902},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tac.2011.2157405","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2011.2157405","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00625401v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00625401","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, 2011, 56 (9), pp.2213-2218. &#x27E8;10.1109/TAC.2011.2157405&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:iris.uniroma1.it:11573/380007","is_oa":false,"landing_page_url":"http://www.scopus.com/inward/record.url?eid=2-s2.0-84865698016&partnerID=65&md5=a8fc3b6db4ea27442efeee689c153e96","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00625401v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00625401","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, 2011, 56 (9), pp.2213-2218. &#x27E8;10.1109/TAC.2011.2157405&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3469518299","display_name":null,"funder_award_id":"CMMI 08-26469","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","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"},{"id":"https://openalex.org/F4320337391","display_name":"Division of Civil, Mechanical and Manufacturing Innovation","ror":"https://ror.org/028yd4c30"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W564609686","https://openalex.org/W614687687","https://openalex.org/W633991252","https://openalex.org/W658670873","https://openalex.org/W1499219562","https://openalex.org/W1502089761","https://openalex.org/W1506119886","https://openalex.org/W1508222939","https://openalex.org/W1979394902","https://openalex.org/W1980137660","https://openalex.org/W1988098342","https://openalex.org/W1991457891","https://openalex.org/W1995877162","https://openalex.org/W1998112257","https://openalex.org/W2019442640","https://openalex.org/W2027304881","https://openalex.org/W2042519843","https://openalex.org/W2050973868","https://openalex.org/W2058572228","https://openalex.org/W2060831685","https://openalex.org/W2067478268","https://openalex.org/W2078761915","https://openalex.org/W2082256594","https://openalex.org/W2088806028","https://openalex.org/W2094833671","https://openalex.org/W2147962536","https://openalex.org/W2148639895","https://openalex.org/W2525143841","https://openalex.org/W3207781852","https://openalex.org/W4243377828","https://openalex.org/W4292872153","https://openalex.org/W6802135958"],"related_works":["https://openalex.org/W2154204858","https://openalex.org/W3209622820","https://openalex.org/W2382250648","https://openalex.org/W2367363545","https://openalex.org/W2586383879","https://openalex.org/W2067895158","https://openalex.org/W2561874146","https://openalex.org/W2066331732","https://openalex.org/W2077468606","https://openalex.org/W4379507409"],"abstract_inverted_index":{"In":[0],"this":[1,114],"note":[2],"the":[3,11,26,43,57,96,108,111,117,127,133,136],"Extended":[4],"Lie":[5],"bracket":[6],"operator":[7],"is":[8,22,129],"introduced":[9],"for":[10,110,121],"analysis":[12],"and":[13,45],"control":[14],"of":[15,29,53,116,126,135,138,151],"nonlinear":[16,54],"time-delay":[17],"systems":[18],"(NLTDS).":[19],"This":[20],"tool":[21],"used":[23,120],"to":[24,102,113,141],"characterize":[25],"integrability":[27],"conditions":[28,47],"a":[30,50,139],"given":[31,51],"submodule.":[32],"The":[33,124],"obtained":[34],"results":[35,128],"have":[36],"two":[37],"fundamental":[38,99],"outcomes.":[39],"First,":[40],"they":[41,106],"define":[42],"necessary":[44],"sufficient":[46],"under":[48],"which":[49],"set":[52,107],"one-forms":[55],"in":[56],"<i":[58,64,68,72,76,80,86],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[59,65,69,73,77,81,87],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</i>":[60],"-dimensional":[61],"delayed":[62],"variables":[63],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">x</i>":[66,74],"(":[67,75],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">t</i>":[70,78],"),...,":[71],"-":[79],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">sD</i>":[82],")":[83],",":[84],"with":[85],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">D</i>":[88],"constant":[89],"but":[90],"unknown,":[91],"are":[92],"integrable,":[93],"thus":[94],"generalizing":[95],"well":[97],"known":[98],"Frobenius":[100],"Theorem":[101],"delay":[103],"systems.":[104,123],"Secondly,":[105],"basis":[109],"extension":[112],"context":[115],"geometric":[118],"approach":[119],"delay-free":[122],"effectiveness":[125],"shown":[130],"by":[131,148],"solving":[132],"problem":[134],"equivalence":[137],"NLTDS":[140],"an":[142],"accessible":[143],"Linear":[144],"Time-Delay":[145],"System":[146],"(LTDS)":[147],"bicausal":[149],"change":[150],"coordinates.":[152]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}