{"id":"https://openalex.org/W2768842961","doi":"https://doi.org/10.1109/tac.2018.2849564","title":"Two Approaches for the Stabilization of Nonlinear KdV Equation With Boundary Time-Delay Feedback","display_name":"Two Approaches for the Stabilization of Nonlinear KdV Equation With Boundary Time-Delay Feedback","publication_year":2018,"publication_date":"2018-06-21","ids":{"openalex":"https://openalex.org/W2768842961","doi":"https://doi.org/10.1109/tac.2018.2849564","mag":"2768842961"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2018.2849564","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2018.2849564","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1711.09696","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058350956","display_name":"Lucie Baudouin","orcid":"https://orcid.org/0000-0002-7181-0321"},"institutions":[{"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"]},{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I17866349","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","ror":"https://ror.org/004raaa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I17866349"]},{"id":"https://openalex.org/I190497903","display_name":"Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes","ror":"https://ror.org/03vcm6439","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I190497903","https://openalex.org/I196454796","https://openalex.org/I205747304","https://openalex.org/I205747304","https://openalex.org/I4210095849","https://openalex.org/I4210159245","https://openalex.org/I4387153255","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Lucie Baudouin","raw_affiliation_strings":["LAAS-CNRS, Universit\u00e9 de Toulouse, CNRS, UPS, Toulouse, France","LAAS-MAC - \u00c9quipe M\u00e9thodes et Algorithmes en Commande (France)"],"affiliations":[{"raw_affiliation_string":"LAAS-CNRS, Universit\u00e9 de Toulouse, CNRS, UPS, Toulouse, France","institution_ids":["https://openalex.org/I134560555","https://openalex.org/I17866349","https://openalex.org/I1294671590","https://openalex.org/I190497903"]},{"raw_affiliation_string":"LAAS-MAC - \u00c9quipe M\u00e9thodes et Algorithmes en Commande (France)","institution_ids":["https://openalex.org/I190497903"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026551038","display_name":"Emmanuelle Cr\u00e9peau","orcid":"https://orcid.org/0000-0002-1149-1955"},"institutions":[{"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"]},{"id":"https://openalex.org/I195731000","display_name":"Universit\u00e9 de Versailles Saint-Quentin-en-Yvelines","ror":"https://ror.org/03mkjjy25","country_code":"FR","type":"education","lineage":["https://openalex.org/I195731000","https://openalex.org/I277688954"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques Blaise Pascal","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]},{"id":"https://openalex.org/I4387152735","display_name":"Laboratoire de Math\u00e9matiques de Versailles","ror":"https://ror.org/04k5jw363","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I195731000","https://openalex.org/I277688954","https://openalex.org/I4387152735"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Emmanuelle Crepeau","raw_affiliation_strings":["LMV, UVSQ, CNRS, Universit\u00e9 Paris-Saclay, Versailles, France","LMV - Laboratoire de Math\u00e9matiques de Versailles (B\u00e2timent Fermat  - UFR de sciences \r\n45 avenue des Etats-Unis\r\n78035 VERSAILLES - France)"],"affiliations":[{"raw_affiliation_string":"LMV, UVSQ, CNRS, Universit\u00e9 Paris-Saclay, Versailles, France","institution_ids":["https://openalex.org/I195731000","https://openalex.org/I277688954","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"LMV - Laboratoire de Math\u00e9matiques de Versailles (B\u00e2timent Fermat  - UFR de sciences \r\n45 avenue des Etats-Unis\r\n78035 VERSAILLES - France)","institution_ids":["https://openalex.org/I4210155549","https://openalex.org/I4387152735"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055249088","display_name":"Julie Valein","orcid":"https://orcid.org/0000-0002-3640-7705"},"institutions":[{"id":"https://openalex.org/I3017839442","display_name":"Institut \u00c9lie Cartan de Lorraine","ror":"https://ror.org/04rvw8791","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I3017839442","https://openalex.org/I4210141950","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Julie Valein","raw_affiliation_strings":["Institut Elie Cartan de Lorraine, Universit\u00e9 de Lorraine & Inria (Project-Team SPHINX), Nancy, France","IECL - Institut \u00c9lie Cartan de Lorraine (Universit\u00e9 de Lorraine, Boulevard des Aiguillettes BP 70239 54506 Vandoeuvre-les-Nancy Cedex\r\nIle du Saulcy - 57 045 Metz Cedex 01 - France)","SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (France)"],"affiliations":[{"raw_affiliation_string":"Institut Elie Cartan de Lorraine, Universit\u00e9 de Lorraine & Inria (Project-Team SPHINX), Nancy, France","institution_ids":["https://openalex.org/I3017839442","https://openalex.org/I90183372"]},{"raw_affiliation_string":"IECL - Institut \u00c9lie Cartan de Lorraine (Universit\u00e9 de Lorraine, Boulevard des Aiguillettes BP 70239 54506 Vandoeuvre-les-Nancy Cedex\r\nIle du Saulcy - 57 045 Metz Cedex 01 - France)","institution_ids":["https://openalex.org/I3017839442","https://openalex.org/I90183372"]},{"raw_affiliation_string":"SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (France)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5058350956"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I17866349","https://openalex.org/I190497903"],"apc_list":null,"apc_paid":null,"fwci":2.8088,"has_fulltext":true,"cited_by_count":48,"citation_normalized_percentile":{"value":0.90764697,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"64","issue":"4","first_page":"1403","last_page":"1414"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":1.0,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":1.0,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9891999959945679,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/observability","display_name":"Observability","score":0.8107014894485474},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7276990413665771},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6880338191986084},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5785335302352905},{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.5746705532073975},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5592007040977478},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5347971320152283},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4546715021133423},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42538586258888245},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4171949625015259},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36974036693573},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13193285465240479},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1289120614528656},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06640946865081787}],"concepts":[{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.8107014894485474},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7276990413665771},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6880338191986084},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5785335302352905},{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.5746705532073975},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5592007040977478},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5347971320152283},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4546715021133423},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42538586258888245},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4171949625015259},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36974036693573},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13193285465240479},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1289120614528656},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06640946865081787},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tac.2018.2849564","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2018.2849564","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:arXiv.org:1711.09696","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.09696","pdf_url":"https://arxiv.org/pdf/1711.09696","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-01643321v1","is_oa":true,"landing_page_url":"https://laas.hal.science/hal-01643321","pdf_url":"https://laas.hal.science/hal-01643321/document","source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","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":"IEEE Transactions on Automatic Control, 2019, 64 (4), pp.1403-1414. ⟨10.1109/TAC.2018.2849564⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1711.09696","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.09696","pdf_url":"https://arxiv.org/pdf/1711.09696","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W46317803","https://openalex.org/W653486459","https://openalex.org/W1527296550","https://openalex.org/W1975993462","https://openalex.org/W1980233447","https://openalex.org/W1980351610","https://openalex.org/W1980366322","https://openalex.org/W1985982935","https://openalex.org/W1986788497","https://openalex.org/W1990834167","https://openalex.org/W1991059830","https://openalex.org/W2011141323","https://openalex.org/W2017307708","https://openalex.org/W2032766396","https://openalex.org/W2042609702","https://openalex.org/W2053082643","https://openalex.org/W2066096538","https://openalex.org/W2066888772","https://openalex.org/W2073078790","https://openalex.org/W2088779465","https://openalex.org/W2091019995","https://openalex.org/W2101694485","https://openalex.org/W2114920878","https://openalex.org/W2115400751","https://openalex.org/W2128039433","https://openalex.org/W2135659811","https://openalex.org/W2157127092","https://openalex.org/W2172250835","https://openalex.org/W2174872450","https://openalex.org/W2178205091","https://openalex.org/W2502764250","https://openalex.org/W2521163219","https://openalex.org/W2612682187","https://openalex.org/W2963666812","https://openalex.org/W3208685521","https://openalex.org/W6621769450","https://openalex.org/W6660451612"],"related_works":["https://openalex.org/W2046459260","https://openalex.org/W2765830098","https://openalex.org/W2967463586","https://openalex.org/W1971989957","https://openalex.org/W2517338020","https://openalex.org/W2154600465","https://openalex.org/W2164703465","https://openalex.org/W2168383058","https://openalex.org/W2143247663","https://openalex.org/W2050693590"],"abstract_inverted_index":{"This":[0],"paper":[1],"concerns":[2],"the":[3,16,19,50,54,73,82,85,89,109,119],"nonlinear":[4,29,55],"Korteweg-de":[5],"Vries":[6],"equation":[7],"with":[8,77,97],"boundary":[9],"time-delay":[10,56],"feedback.":[11],"Under":[12],"appropriate":[13],"assumption":[14,80],"on":[15,72,81,108],"coefficients":[17],"of":[18,43,53,84,88],"feedbacks":[20],"(delayed":[21],"or":[22],"not),":[23],"we":[24],"first":[25],"prove":[26],"that":[27],"this":[28],"infinite":[30],"dimensional":[31],"system":[32],"is":[33],"well":[34],"posed":[35],"for":[36],"small":[37],"initial":[38],"data.":[39],"The":[40],"main":[41],"results":[42],"our":[44],"study":[45],"are":[46,61,115],"two":[47],"theorems":[48],"stating":[49],"exponential":[51],"stability":[52],"system.":[57],"Two":[58],"different":[59],"methods":[60],"employed:":[62],"a":[63,78,98],"Lyapunov":[64],"function":[65],"approach":[66],"(allowing":[67],"to":[68,117],"have":[69],"an":[70,93],"estimation":[71,107],"decay":[74,110],"rate,":[75],"but":[76,105],"restrictive":[79],"length":[83],"spatial":[86],"domain":[87],"KdV":[90],"equation)":[91],"and":[92],"observability":[94],"inequality":[95],"approach,":[96],"contradiction":[99],"argument":[100],"(for":[101],"any":[102],"noncritical":[103],"lengths":[104],"without":[106],"rate).":[111],"Some":[112],"numerical":[113],"simulations":[114],"given":[116],"illustrate":[118],"results.":[120]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":7}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}