{"id":"https://openalex.org/W2507860018","doi":"https://doi.org/10.1109/cdc.2016.7798238","title":"Time scale modeling for consensus in sparse directed networks with time-varying topologies","display_name":"Time scale modeling for consensus in sparse directed networks with time-varying topologies","publication_year":2016,"publication_date":"2016-12-01","ids":{"openalex":"https://openalex.org/W2507860018","doi":"https://doi.org/10.1109/cdc.2016.7798238","mag":"2507860018"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2016.7798238","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2016.7798238","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE 55th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1608.08384","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069674349","display_name":"Samuel Mart\u00edn","orcid":"https://orcid.org/0000-0003-0289-6317"},"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/I4210110792","display_name":"Centre de Recherche en Automatique de Nancy","ror":"https://ror.org/022r5hc56","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210099203","https://openalex.org/I4210100260","https://openalex.org/I4210110792","https://openalex.org/I4210159245","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":"Samuel Martin","raw_affiliation_strings":["Universit\u00e9 de Lorraine, CRAN, UMR 7039, and CNRS, CRAN, UMR 7039, Vandxuvre, France","Universit\u00e9 de Lorraine, CRAN, UMR 7039, 2, Avenue de la For\u00eat de Haye, 54500, Vand\u0153uvre, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Lorraine, CRAN, UMR 7039, and CNRS, CRAN, UMR 7039, Vandxuvre, France","institution_ids":["https://openalex.org/I90183372","https://openalex.org/I1294671590","https://openalex.org/I4210110792"]},{"raw_affiliation_string":"Universit\u00e9 de Lorraine, CRAN, UMR 7039, 2, Avenue de la For\u00eat de Haye, 54500, Vand\u0153uvre, France","institution_ids":["https://openalex.org/I4210110792","https://openalex.org/I90183372"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078506595","display_name":"Irinel\u2010Constantin Mor\u0103rescu","orcid":null},"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/I4210110792","display_name":"Centre de Recherche en Automatique de Nancy","ror":"https://ror.org/022r5hc56","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210099203","https://openalex.org/I4210100260","https://openalex.org/I4210110792","https://openalex.org/I4210159245","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":"Irinel-Constantin Morarescu","raw_affiliation_strings":["Universit\u00e9 de Lorraine, CRAN, UMR 7039, and CNRS, CRAN, UMR 7039, Vandxuvre, France","Universit\u00e9 de Lorraine, CRAN, UMR 7039, 2, Avenue de la For\u00eat de Haye, 54500, Vand\u0153uvre, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Lorraine, CRAN, UMR 7039, and CNRS, CRAN, UMR 7039, Vandxuvre, France","institution_ids":["https://openalex.org/I90183372","https://openalex.org/I1294671590","https://openalex.org/I4210110792"]},{"raw_affiliation_string":"Universit\u00e9 de Lorraine, CRAN, UMR 7039, 2, Avenue de la For\u00eat de Haye, 54500, Vand\u0153uvre, France","institution_ids":["https://openalex.org/I4210110792","https://openalex.org/I90183372"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035230630","display_name":"Dragan Ne\u0161i\u0107","orcid":"https://orcid.org/0000-0001-7944-0241"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"The University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Dragan Nesic","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, VIC, Australia","Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, 3010 VIC, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, VIC, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, 3010 VIC, Australia","institution_ids":["https://openalex.org/I165779595"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"7","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9995999932289124,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9995999932289124,"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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9957000017166138,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.7313365340232849},{"id":"https://openalex.org/keywords/aggregate","display_name":"Aggregate (composite)","score":0.6240261793136597},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5470037460327148},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5033850073814392},{"id":"https://openalex.org/keywords/strongly-connected-component","display_name":"Strongly connected component","score":0.4741843640804291},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.4740930497646332},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4632403254508972},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.45775094628334045},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.43698593974113464},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.42897284030914307},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.41935092210769653},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.41907158493995667},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4016752243041992},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3905412256717682},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32125598192214966},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.190363347530365},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1685815453529358}],"concepts":[{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.7313365340232849},{"id":"https://openalex.org/C4679612","wikidata":"https://www.wikidata.org/wiki/Q866298","display_name":"Aggregate (composite)","level":2,"score":0.6240261793136597},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5470037460327148},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5033850073814392},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.4741843640804291},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.4740930497646332},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4632403254508972},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.45775094628334045},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.43698593974113464},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.42897284030914307},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.41935092210769653},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.41907158493995667},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4016752243041992},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3905412256717682},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32125598192214966},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.190363347530365},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1685815453529358},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"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/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","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/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/cdc.2016.7798238","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2016.7798238","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE 55th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1608.08384","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1608.08384","pdf_url":"https://arxiv.org/pdf/1608.08384","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:arXiv.org:1608.08384","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1608.08384","pdf_url":"https://arxiv.org/pdf/1608.08384","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":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-01379076v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01379076","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":"http://cdc2016.ieeecss.org/","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"doi:10.48550/arxiv.1608.08384","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1608.08384","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1608.08384","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1608.08384","pdf_url":"https://arxiv.org/pdf/1608.08384","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":[{"id":"https://openalex.org/G4889790396","display_name":null,"funder_award_id":"PEPS INS2I","funder_id":"https://openalex.org/F4320322892","funder_display_name":"Centre National de la Recherche Scientifique"},{"id":"https://openalex.org/G6262155132","display_name":null,"funder_award_id":"ANR-13-BS03-004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"},{"id":"https://openalex.org/F4320336508","display_name":"Institut des sciences de l'information et de leurs interactions","ror":"https://ror.org/04z22qz54"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W86892992","https://openalex.org/W1515224583","https://openalex.org/W1590821414","https://openalex.org/W1905235987","https://openalex.org/W1981870190","https://openalex.org/W2015385256","https://openalex.org/W2022705484","https://openalex.org/W2022803583","https://openalex.org/W2028706574","https://openalex.org/W2030205386","https://openalex.org/W2094357153","https://openalex.org/W2107396783","https://openalex.org/W2108875766","https://openalex.org/W2123326271","https://openalex.org/W2154217311","https://openalex.org/W2179502718","https://openalex.org/W2180822344","https://openalex.org/W2964198956","https://openalex.org/W4248220600","https://openalex.org/W4293078920","https://openalex.org/W6635480729"],"related_works":["https://openalex.org/W3152517103","https://openalex.org/W1583825963","https://openalex.org/W2018786233","https://openalex.org/W1623426772","https://openalex.org/W1495236997","https://openalex.org/W2034099022","https://openalex.org/W3126567023","https://openalex.org/W2073084601","https://openalex.org/W2039837136","https://openalex.org/W2308586727","https://openalex.org/W3212653422","https://openalex.org/W2105448342","https://openalex.org/W1553521088","https://openalex.org/W110901151","https://openalex.org/W3100658280","https://openalex.org/W3103893677","https://openalex.org/W3034097400","https://openalex.org/W2952271679","https://openalex.org/W2583860964","https://openalex.org/W2270504642"],"abstract_inverted_index":{"The":[0,91],"paper":[1],"considers":[2],"the":[3,29,51,54,79,102,115,121,124,133,143,160,168,178,198],"consensus":[4],"problem":[5],"in":[6,56,82,114,126,170],"large":[7,83],"networks":[8,21,84],"represented":[9],"by":[10,27,196],"time-varying":[11,107,156,181],"directed":[12,108,182],"graphs.":[13,90],"A":[14],"practical":[15],"way":[16],"of":[17,31,53,93,106,123,167,200],"dealing":[18],"with":[19,177,188],"large-scale":[20],"is":[22,96,111,129,147,194],"to":[23,34,68,74,97,101,158,175,207],"reduce":[24],"their":[25],"dimension":[26],"collapsing":[28],"states":[30,52,125,169],"nodes":[32],"belonging":[33],"densely":[35],"and":[36,88,117],"intensively":[37],"connected":[38],"clusters":[39],"into":[40],"aggregate":[41,69,144,161],"variables.":[42,145],"It":[43,110],"will":[44],"be":[45],"shown":[46],"that":[47,113],"under":[48],"suitable":[49,155],"conditions,":[50],"agents":[55],"each":[57,127,171],"cluster":[58,128],"converge":[59,73],"fast":[60],"toward":[61],"a":[62,189],"local":[63],"agreement.":[64],"Local":[65],"agreements":[66],"correspond":[67],"variables":[70,162],"which":[71,193,204],"slowly":[72],"consensus.":[75],"Existing":[76],"results":[77,100],"concerning":[78],"time-scale":[80],"separation":[81],"focus":[85],"on":[86],"fixed":[87,116],"undirected":[89,118],"aim":[92],"this":[94,208],"work":[95],"extend":[98],"these":[99],"more":[103,179],"general":[104],"case":[105,120],"topologies.":[109],"noteworthy":[112],"graph":[119,183],"average":[122],"time-invariant":[130,164],"when":[131],"neglecting":[132],"interactions":[134],"between":[135],"clusters.":[136],"Therefore,":[137],"they":[138],"are":[139],"good":[140],"candidates":[141],"for":[142],"This":[146,173],"no":[148],"longer":[149],"possible":[150],"here.":[151],"Instead,":[152],"we":[153],"find":[154],"weights":[157],"compute":[159],"as":[163],"weighted":[165],"averages":[166],"cluster.":[172],"allows":[174],"deal":[176],"challenging":[180],"case.":[184],"We":[185],"end":[186],"up":[187],"singularly":[190],"perturbed":[191],"system":[192],"analyzed":[195],"using":[197],"tools":[199],"two":[201],"time-scales":[202],"averaging":[203],"seem":[205],"appropriate":[206],"system.":[209]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2016-09-16T00:00:00"}