{"id":"https://openalex.org/W2626984388","doi":"https://doi.org/10.1109/tac.2017.2730485","title":"Stability of Linear Systems With Time-Varying Delays Using Bessel\u2013Legendre Inequalities","display_name":"Stability of Linear Systems With Time-Varying Delays Using Bessel\u2013Legendre Inequalities","publication_year":2017,"publication_date":"2017-07-21","ids":{"openalex":"https://openalex.org/W2626984388","doi":"https://doi.org/10.1109/tac.2017.2730485","mag":"2626984388"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2017.2730485","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2017.2730485","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://laas.hal.science/hal-01537184","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029842446","display_name":"Alexandre Seuret","orcid":"https://orcid.org/0000-0003-1434-7614"},"institutions":[{"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/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555","https://openalex.org/I4405258862"]},{"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/I134560555","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","https://openalex.org/I4405258862"]},{"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":true,"raw_author_name":"Alexandre Seuret","raw_affiliation_strings":["Laboratory for Analysis and Architecture of Systems - CNRS, Universit\u00e9 de Toulouse, CNRS, UPS, Toulouse, France","LAAS-MAC - \u00c9quipe M\u00e9thodes et Algorithmes en Commande (France)"],"affiliations":[{"raw_affiliation_string":"Laboratory for Analysis and Architecture of Systems - CNRS, Universit\u00e9 de Toulouse, CNRS, UPS, Toulouse, France","institution_ids":["https://openalex.org/I190497903","https://openalex.org/I17866349","https://openalex.org/I134560555","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"LAAS-MAC - \u00c9quipe M\u00e9thodes et Algorithmes en Commande (France)","institution_ids":["https://openalex.org/I190497903"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067899511","display_name":"Fr\u00e9d\u00e9ric Gouaisbaut","orcid":"https://orcid.org/0000-0002-4263-7195"},"institutions":[{"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/I134560555","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","https://openalex.org/I4405258862"]},{"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","https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Frederic Gouaisbaut","raw_affiliation_strings":["Laboratory for Analysis and Architecture of Systems - CNRS, Universit\u00e9 de Toulouse, CNRS, UPS, Toulouse, France","LAAS-MAC - \u00c9quipe M\u00e9thodes et Algorithmes en Commande (France)"],"affiliations":[{"raw_affiliation_string":"Laboratory for Analysis and Architecture of Systems - CNRS, Universit\u00e9 de Toulouse, CNRS, UPS, Toulouse, France","institution_ids":["https://openalex.org/I190497903","https://openalex.org/I17866349","https://openalex.org/I134560555","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"LAAS-MAC - \u00c9quipe M\u00e9thodes et Algorithmes en Commande (France)","institution_ids":["https://openalex.org/I190497903"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5029842446"],"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":21.3794,"has_fulltext":false,"cited_by_count":359,"citation_normalized_percentile":{"value":0.99660503,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"63","issue":"1","first_page":"225","last_page":"232"},"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":0.9995999932289124,"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":0.9995999932289124,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9854999780654907,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.725580096244812},{"id":"https://openalex.org/keywords/bessel-function","display_name":"Bessel function","score":0.7248375415802002},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7188462018966675},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6439343094825745},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5507494211196899},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.52577805519104},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5193199515342712},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.4895816743373871},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.44410327076911926},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.39430665969848633},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30452823638916016},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21037662029266357}],"concepts":[{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.725580096244812},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.7248375415802002},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7188462018966675},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6439343094825745},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5507494211196899},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.52577805519104},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5193199515342712},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.4895816743373871},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.44410327076911926},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.39430665969848633},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30452823638916016},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21037662029266357},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2017.2730485","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2017.2730485","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-01537184v1","is_oa":true,"landing_page_url":"https://laas.hal.science/hal-01537184","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, 2018, 63 (1), pp.225-232. &#x27E8;10.1109/TAC.2017.2730485&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01537184v1","is_oa":true,"landing_page_url":"https://laas.hal.science/hal-01537184","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, 2018, 63 (1), pp.225-232. &#x27E8;10.1109/TAC.2017.2730485&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.44999998807907104,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W85072216","https://openalex.org/W325253995","https://openalex.org/W1506119886","https://openalex.org/W1541913511","https://openalex.org/W1545352440","https://openalex.org/W1963839355","https://openalex.org/W1965587013","https://openalex.org/W1969471037","https://openalex.org/W1981673401","https://openalex.org/W1986582332","https://openalex.org/W2016562720","https://openalex.org/W2037686415","https://openalex.org/W2050098163","https://openalex.org/W2054534795","https://openalex.org/W2059279280","https://openalex.org/W2061996363","https://openalex.org/W2097114089","https://openalex.org/W2103774239","https://openalex.org/W2109310060","https://openalex.org/W2126999594","https://openalex.org/W2129546905","https://openalex.org/W2149971042","https://openalex.org/W2150453753","https://openalex.org/W2173039830","https://openalex.org/W2358432708","https://openalex.org/W2544001552","https://openalex.org/W2745726220","https://openalex.org/W4240729697"],"related_works":["https://openalex.org/W2049939404","https://openalex.org/W2736737644","https://openalex.org/W1519777678","https://openalex.org/W2034875467","https://openalex.org/W76811607","https://openalex.org/W2011121568","https://openalex.org/W3106446297","https://openalex.org/W4388316559","https://openalex.org/W1848405970","https://openalex.org/W2056877771"],"abstract_inverted_index":{"This":[0],"paper":[1,52],"addresses":[2],"the":[3,28,54,64,67,72,99],"stability":[4,14,68],"problem":[5],"of":[6,27,35,63,66,82],"linear":[7,18],"systems":[8],"with":[9],"a":[10,79],"time-varying":[11,58],"delay.":[12],"Hierarchical":[13],"conditions":[15],"based":[16],"on":[17,70,98],"matrix":[19],"inequalities":[20],"are":[21],"obtained":[22],"from":[23],"an":[24],"extensive":[25],"use":[26],"Bessel":[29],"inequality":[30,40],"applied":[31],"to":[32,57,77,95],"Legendre":[33],"polynomials":[34],"arbitrary":[36],"orders.":[37],"While":[38],"this":[39,51],"has":[41],"been":[42],"only":[43],"used":[44],"for":[45],"constant":[46],"discrete":[47],"and":[48,74,88],"distributed":[49],"delays,":[50],"generalizes":[53],"same":[55],"methodology":[56],"delays.":[59],"We":[60],"take":[61],"advantages":[62],"dependence":[65],"criteria":[69],"both":[71],"delay":[73,84],"its":[75],"derivative":[76],"propose":[78],"new":[80],"definition":[81,93],"allowable":[83],"sets.":[85],"A":[86],"light":[87],"smart":[89],"modification":[90],"in":[91],"their":[92],"leads":[94],"relevant":[96],"conclusions":[97],"numerical":[100],"results.":[101]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":29},{"year":2024,"cited_by_count":58},{"year":2023,"cited_by_count":46},{"year":2022,"cited_by_count":51},{"year":2021,"cited_by_count":62},{"year":2020,"cited_by_count":38},{"year":2019,"cited_by_count":43},{"year":2018,"cited_by_count":23},{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-22T08:09:32.410652","created_date":"2025-10-10T00:00:00"}
