{"id":"https://openalex.org/W3109964466","doi":"https://doi.org/10.1109/tsmc.2020.3030782","title":"Robust Cluster Synchronization in Dynamical Networks With Directed Switching Topology via Averaging Method","display_name":"Robust Cluster Synchronization in Dynamical Networks With Directed Switching Topology via Averaging Method","publication_year":2020,"publication_date":"2020-11-25","ids":{"openalex":"https://openalex.org/W3109964466","doi":"https://doi.org/10.1109/tsmc.2020.3030782","mag":"3109964466"},"language":"en","primary_location":{"id":"doi:10.1109/tsmc.2020.3030782","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2020.3030782","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"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 Systems, Man, and Cybernetics: Systems","raw_type":"journal-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/A5102920216","display_name":"Ku Du","orcid":"https://orcid.org/0000-0002-8980-4149"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ku Du","raw_affiliation_strings":["University of Science and Technology of China, Hefei, China"],"raw_orcid":"https://orcid.org/0000-0002-8980-4149","affiliations":[{"raw_affiliation_string":"University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101997909","display_name":"Qichao Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qichao Ma","raw_affiliation_strings":["University of Science and Technology of China, Hefei, China"],"raw_orcid":"https://orcid.org/0000-0002-4861-3565","affiliations":[{"raw_affiliation_string":"University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025987638","display_name":"Yu Kang","orcid":"https://orcid.org/0000-0002-8706-3252"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu Kang","raw_affiliation_strings":["State Key Laboratory of Fire Science, Institute of Advanced Technology, University of Science and Technology of China, Hefei, China"],"raw_orcid":"https://orcid.org/0000-0002-8706-3252","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Fire Science, Institute of Advanced Technology, University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032772849","display_name":"Weiming Fu","orcid":"https://orcid.org/0000-0002-3576-3126"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weiming Fu","raw_affiliation_strings":["University of Science and Technology of China, Hefei, China"],"raw_orcid":"https://orcid.org/0000-0002-3576-3126","affiliations":[{"raw_affiliation_string":"University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4586,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.84069484,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"52","issue":"3","first_page":"1694","last_page":"1704"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9998999834060669,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9998999834060669,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9994000196456909,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9984999895095825,"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/topology","display_name":"Topology (electrical circuits)","score":0.7401541471481323},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.6152935028076172},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6056790351867676},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.5924863219261169},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.5153667330741882},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4827079772949219},{"id":"https://openalex.org/keywords/extension-topology","display_name":"Extension topology","score":0.47938990592956543},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.4691428542137146},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4625737965106964},{"id":"https://openalex.org/keywords/weak-topology","display_name":"Weak topology (polar topology)","score":0.4542340636253357},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.4386095404624939},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4037018418312073},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3559795320034027},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3523018956184387},{"id":"https://openalex.org/keywords/general-topology","display_name":"General topology","score":0.21345564723014832},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.09227427840232849},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07729008793830872},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07626363635063171},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.06344810128211975}],"concepts":[{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.7401541471481323},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.6152935028076172},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6056790351867676},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.5924863219261169},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.5153667330741882},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4827079772949219},{"id":"https://openalex.org/C143913944","wikidata":"https://www.wikidata.org/wiki/Q5421952","display_name":"Extension topology","level":4,"score":0.47938990592956543},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.4691428542137146},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4625737965106964},{"id":"https://openalex.org/C129866940","wikidata":"https://www.wikidata.org/wiki/Q505760","display_name":"Weak topology (polar topology)","level":5,"score":0.4542340636253357},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.4386095404624939},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4037018418312073},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3559795320034027},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3523018956184387},{"id":"https://openalex.org/C129089157","wikidata":"https://www.wikidata.org/wiki/Q621550","display_name":"General topology","level":3,"score":0.21345564723014832},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.09227427840232849},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07729008793830872},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07626363635063171},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.06344810128211975},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsmc.2020.3030782","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2020.3030782","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"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 Systems, Man, and Cybernetics: Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2339939468","display_name":null,"funder_award_id":"2018YFE0106800","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G3466844949","display_name":null,"funder_award_id":"2018AAA0100800","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G6110658884","display_name":null,"funder_award_id":"61725304","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8871303421","display_name":null,"funder_award_id":"61673361","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1987924998","https://openalex.org/W1988095001","https://openalex.org/W1997974219","https://openalex.org/W2009702937","https://openalex.org/W2016910787","https://openalex.org/W2019229544","https://openalex.org/W2021444019","https://openalex.org/W2024236739","https://openalex.org/W2039313558","https://openalex.org/W2044319005","https://openalex.org/W2047283311","https://openalex.org/W2053769764","https://openalex.org/W2100935517","https://openalex.org/W2117817591","https://openalex.org/W2134889984","https://openalex.org/W2145206324","https://openalex.org/W2154953441","https://openalex.org/W2167822639","https://openalex.org/W2293710996","https://openalex.org/W2388591084","https://openalex.org/W2517050798","https://openalex.org/W2529002166","https://openalex.org/W2581258406","https://openalex.org/W2606690472","https://openalex.org/W2793101123","https://openalex.org/W2805542056","https://openalex.org/W2940501546","https://openalex.org/W2947553656","https://openalex.org/W2966106606","https://openalex.org/W3005135630","https://openalex.org/W4229706427"],"related_works":["https://openalex.org/W2963837678","https://openalex.org/W4301479830","https://openalex.org/W2515833534","https://openalex.org/W51146019","https://openalex.org/W2163446102","https://openalex.org/W2941717049","https://openalex.org/W2506260474","https://openalex.org/W2049776876","https://openalex.org/W2126785047","https://openalex.org/W83450382"],"abstract_inverted_index":{"This":[0],"article":[1],"investigates":[2],"a":[3,32,49,83,115,127,182,192],"bounded":[4,185],"cluster":[5,28,123,186],"synchronization":[6,124,187],"problem":[7,125,129],"of":[8,14,51,96,144,175],"dynamical":[9,68,145],"systems,":[10],"which":[11,35,61],"can":[12,188],"be":[13,79,189],"the":[15,37,41,56,63,67,73,97,102,107,122,131,138,151,155,171,176],"generic":[16],"linear":[17,195],"type":[18],"or":[19,196],"Lipschitz":[20],"nonlinear":[21,197],"type,":[22],"over":[23,86],"directed":[24,116],"switching":[25,194],"network.":[26],"Each":[27],"is":[29,46,53,76,111,135,147,167,179],"equipped":[30],"with":[31,82],"virtual":[33,74,104],"leader":[34],"produces":[36],"desired":[38],"trajectory":[39],"for":[40,141,191],"agents":[42,98],"to":[43,78,113,162,203],"track.":[44],"It":[45,134],"required":[47,112],"only":[48],"fraction":[50],"systems":[52,69,146],"influenced":[54],"by":[55,150],"leader.":[57],"The":[58],"interaction":[59],"topology,":[60],"describes":[62],"information":[64],"exchange":[65],"among":[66],"as":[70,72,99,101],"well":[71,100],"leaders,":[75],"allowed":[77],"time":[80],"varying":[81],"well-defined":[84],"average":[85],"an":[87],"infinite":[88],"horizon.":[89],"That":[90],"is,":[91],"each":[92],"augmented":[93],"cluster,":[94],"consisting":[95],"corresponding":[103],"leader,":[105],"in":[106],"time-average":[108,177],"network":[109,156],"topology":[110,157,178],"have":[114],"spanning":[117],"tree.":[118],"We":[119],"then":[120,184],"transform":[121],"into":[126],"stability":[128],"via":[130],"averaging":[132,152],"method.":[133],"proved":[136],"that":[137,169],"convergence":[139],"property":[140],"both":[142],"types":[143],"exclusively":[148],"determined":[149],"system":[153],"if":[154,170],"switches":[158],"sufficiently":[159],"fast":[160,193],"compared":[161],"original":[163],"systems.":[164,198],"Finally,":[165],"it":[166],"concluded":[168],"intracluster":[172],"coupling":[173],"strength":[174],"stronger":[180],"than":[181],"threshold,":[183],"realized":[190],"Two":[199],"examples":[200],"are":[201],"provided":[202],"verify":[204],"our":[205],"results.":[206]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
