{"id":"https://openalex.org/W2576060072","doi":"https://doi.org/10.1109/ecc.2016.7810535","title":"Migration of imaginary roots of multiplicity three and four under small deviation of two delays in time-delay systems","display_name":"Migration of imaginary roots of multiplicity three and four under small deviation of two delays in time-delay systems","publication_year":2016,"publication_date":"2016-06-01","ids":{"openalex":"https://openalex.org/W2576060072","doi":"https://doi.org/10.1109/ecc.2016.7810535","mag":"2576060072"},"language":"en","primary_location":{"id":"doi:10.1109/ecc.2016.7810535","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ecc.2016.7810535","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 European Control Conference (ECC)","raw_type":"proceedings-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/A5053571082","display_name":"Dina Irofti","orcid":"https://orcid.org/0000-0002-9254-7980"},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]},{"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":true,"raw_author_name":"Dina Irofti","raw_affiliation_strings":["Universite Paris-Sud, Orsay, \u00c3\u017dle-de-France, FR","L2S - Laboratoire des signaux et syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"Universite Paris-Sud, Orsay, \u00c3\u017dle-de-France, FR","institution_ids":["https://openalex.org/I102197404"]},{"raw_affiliation_string":"L2S - Laboratoire des signaux et syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)","institution_ids":["https://openalex.org/I4210097418"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086584348","display_name":"Keqin Gu","orcid":"https://orcid.org/0000-0003-2587-4284"},"institutions":[{"id":"https://openalex.org/I87547150","display_name":"Southern Illinois University Edwardsville","ror":"https://ror.org/04cqs5j56","country_code":"US","type":"education","lineage":["https://openalex.org/I2801502357","https://openalex.org/I87547150"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Keqin Gu","raw_affiliation_strings":["Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, Illinois, USA","Department of Mechanical and Industrial Engineering (United States)"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, Illinois, USA","institution_ids":["https://openalex.org/I87547150"]},{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering (United States)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016703524","display_name":"Islam Boussaada","orcid":"https://orcid.org/0000-0001-7020-6395"},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]},{"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"]},{"id":"https://openalex.org/I58581550","display_name":"Institut Polytechnique des Sciences Avanc\u00e9es","ror":"https://ror.org/050r7zc91","country_code":"FR","type":"education","lineage":["https://openalex.org/I58581550"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Islam Boussaada","raw_affiliation_strings":["Universite Paris-Sud, Orsay, \u00c3\u017dle-de-France, FR","L2S - Laboratoire des signaux et syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)","IPSA - Institut Polytechnique des Sciences Avanc\u00e9es (5-9 rue Maurice Grandcoing 94200 Ivry-sur-Seine - France)"],"affiliations":[{"raw_affiliation_string":"Universite Paris-Sud, Orsay, \u00c3\u017dle-de-France, FR","institution_ids":["https://openalex.org/I102197404"]},{"raw_affiliation_string":"L2S - Laboratoire des signaux et syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)","institution_ids":["https://openalex.org/I4210097418"]},{"raw_affiliation_string":"IPSA - Institut Polytechnique des Sciences Avanc\u00e9es (5-9 rue Maurice Grandcoing 94200 Ivry-sur-Seine - France)","institution_ids":["https://openalex.org/I58581550"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058754609","display_name":"Silviu\u2010Iulian Niculescu","orcid":"https://orcid.org/0000-0002-3444-2566"},"institutions":[{"id":"https://openalex.org/I4210107720","display_name":"CentraleSup\u00e9lec","ror":"https://ror.org/019tcpt25","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I4210107720"]},{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]},{"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":"Silviu-Iulian Niculescu","raw_affiliation_strings":["Universite Paris-Sud, Orsay, \u00c3\u017dle-de-France, FR","DISCO - Dynamical Interconnected Systems in COmplex Environments (CentraleSupelec\r\n3 rue Joliot-Curie 91192 Gif-sur-Yvette cedex - France)","L2S - Laboratoire des signaux et syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"Universite Paris-Sud, Orsay, \u00c3\u017dle-de-France, FR","institution_ids":["https://openalex.org/I102197404"]},{"raw_affiliation_string":"DISCO - Dynamical Interconnected Systems in COmplex Environments (CentraleSupelec\r\n3 rue Joliot-Curie 91192 Gif-sur-Yvette cedex - France)","institution_ids":["https://openalex.org/I4210107720"]},{"raw_affiliation_string":"L2S - Laboratoire des signaux et syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)","institution_ids":["https://openalex.org/I4210097418"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5053571082"],"corresponding_institution_ids":["https://openalex.org/I102197404","https://openalex.org/I4210097418"],"apc_list":null,"apc_paid":null,"fwci":0.8686,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.79051463,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"i and ii","issue":null,"first_page":"1697","last_page":"1702"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13983","display_name":"Cybersecurity and Information Systems","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13983","display_name":"Cybersecurity and Information Systems","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9904000163078308,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9843999743461609,"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/multiplicity","display_name":"Multiplicity (mathematics)","score":0.7143599390983582},{"id":"https://openalex.org/keywords/the-imaginary","display_name":"The Imaginary","score":0.5777978301048279},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41113027930259705},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38423728942871094},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26336973905563354}],"concepts":[{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.7143599390983582},{"id":"https://openalex.org/C135068731","wikidata":"https://www.wikidata.org/wiki/Q1169049","display_name":"The Imaginary","level":2,"score":0.5777978301048279},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41113027930259705},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38423728942871094},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26336973905563354},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/ecc.2016.7810535","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ecc.2016.7810535","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 European Control Conference (ECC)","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-01418212v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01418212","pdf_url":null,"source":{"id":"https://openalex.org/S4406922461","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":"http://www.ecc16.eu/index.shtml","raw_type":"Conference papers"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.550000011920929,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W561938405","https://openalex.org/W658670873","https://openalex.org/W1575147392","https://openalex.org/W1974988149","https://openalex.org/W1989107982","https://openalex.org/W1989251100","https://openalex.org/W2017776242","https://openalex.org/W2022419653","https://openalex.org/W2048056120","https://openalex.org/W2074178424","https://openalex.org/W2075114996","https://openalex.org/W2080529473","https://openalex.org/W2149519244","https://openalex.org/W2291413787","https://openalex.org/W2588297134","https://openalex.org/W2977318642","https://openalex.org/W4232216300","https://openalex.org/W6621726870"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W3016733773","https://openalex.org/W2491088243","https://openalex.org/W1979400567","https://openalex.org/W2353064048","https://openalex.org/W2000265659","https://openalex.org/W2754367428","https://openalex.org/W4389942819","https://openalex.org/W2982365196"],"abstract_inverted_index":{"This":[0],"paper":[1,53],"studies":[2],"the":[3,22,54,64,72,83,97,109,118,121,124,137,141,147,151,157,161,165,170,177,182,187],"migration":[4],"pattern":[5],"of":[6,10,66,102,120,169],"characteristic":[7],"imaginary":[8],"roots":[9,41,88,144,154,171],"multiplicity":[11],"three":[12,168],"and":[13,93,133,150,176],"four":[14],"in":[15,51,82,117,130],"time-delay":[16],"systems":[17],"with":[18,45],"two":[19,87,143,153],"delays":[20],"when":[21,78],"delay":[23,48,84,125],"parameters":[24,138,162],"undergo":[25],"small":[26],"deviations.":[27],"Stability":[28],"analysis":[29],"for":[30],"such":[31],"problems":[32],"is":[33,56,105,128],"often":[34],"based":[35],"on":[36,186],"Puiseux":[37,61],"series,":[38],"as":[39,108],"multiple":[40],"are":[42,76],"not":[43],"differentiable":[44],"respect":[46],"to":[47,90,96,146,156,173,181],"parameters.":[49],"However,":[50],"this":[52],"approach":[55],"more":[57,106],"traditional":[58],"without":[59],"using":[60],"series.":[62],"In":[63],"case":[65,101],"triple":[67],"roots,":[68],"we":[69],"show":[70],"that":[71],"stability":[73,110],"crossing":[74,111],"curves":[75],"smooth;":[77],"a":[79,114,134],"perturbation":[80],"occurs":[81],"parameter":[85,126],"space,":[86],"move":[89,139,145,155,163,172],"one":[91,94,174],"half-plane":[92],"root":[95,104,179],"other":[98,152,183],"half-plane.":[99,159],"The":[100],"quadruple":[103],"complicated":[107],"curve":[112],"has":[113],"cusp.":[115],"Thus,":[116],"neighbourhood":[119],"critical":[122],"point,":[123],"space":[127],"divided":[129],"an":[131],"S-sector":[132],"G-sector.":[135],"When":[136,160],"into":[140,164],"G-sector,":[142],"right":[148],"half-plane,":[149,175,184],"left":[158],"S-sector,":[166],"then":[167],"remaining":[178],"moves":[180],"depending":[185],"conditions.":[188]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-02-27T16:54:17.756197","created_date":"2025-10-10T00:00:00"}
