{"id":"https://openalex.org/W4408519640","doi":"https://doi.org/10.1109/tcsi.2025.3539893","title":"Retraction Notice: Robustness Margins for Attainable Consensusability of Unstable Multi-Agent Systems: Output Consensus Protocols Over Directed Network Topology","display_name":"Retraction Notice: Robustness Margins for Attainable Consensusability of Unstable Multi-Agent Systems: Output Consensus Protocols Over Directed Network Topology","publication_year":2025,"publication_date":"2025-03-17","ids":{"openalex":"https://openalex.org/W4408519640","doi":"https://doi.org/10.1109/tcsi.2025.3539893"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2025.3539893","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2025.3539893","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"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 Circuits and Systems I: Regular Papers","raw_type":"journal-article"},"type":"retraction","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/A5061390982","display_name":"Qi Mao","orcid":"https://orcid.org/0000-0001-8513-5577"},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qi Mao","raw_affiliation_strings":["School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, China","institution_ids":["https://openalex.org/I152031979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084240132","display_name":"S. W. Li","orcid":"https://orcid.org/0009-0006-1247-0976"},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shi Li","raw_affiliation_strings":["School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, China","institution_ids":["https://openalex.org/I152031979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073397536","display_name":"Guobao Liu","orcid":"https://orcid.org/0000-0002-8553-6167"},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guobao Liu","raw_affiliation_strings":["School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, China","institution_ids":["https://openalex.org/I152031979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044375216","display_name":"Liqian Dou","orcid":"https://orcid.org/0000-0002-3979-0420"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liqian Dou","raw_affiliation_strings":["School of Electrical and Information Engineering, Tianjin University, Tianjin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Information Engineering, Tianjin University, Tianjin, China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003234602","display_name":"Bailing Tian","orcid":"https://orcid.org/0000-0003-1004-8350"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bailing Tian","raw_affiliation_strings":["School of Electrical and Information Engineering, Tianjin University, Tianjin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Information Engineering, Tianjin University, Tianjin, China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073871408","display_name":"Qun Zong","orcid":"https://orcid.org/0000-0003-0734-6728"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qun Zong","raw_affiliation_strings":["School of Electrical and Information Engineering, Tianjin University, Tianjin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Information Engineering, Tianjin University, Tianjin, China","institution_ids":["https://openalex.org/I162868743"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"5","first_page":"2481","last_page":"2481"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12784","display_name":"Modular Robots and Swarm Intelligence","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T12784","display_name":"Modular Robots and Swarm Intelligence","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T10772","display_name":"Distributed systems and fault tolerance","score":0.9969000220298767,"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":0.9950000047683716,"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/notice","display_name":"Notice","score":0.8200214505195618},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.7572311758995056},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.6432428359985352},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.59397292137146},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5552802681922913},{"id":"https://openalex.org/keywords/multi-agent-system","display_name":"Multi-agent system","score":0.5387559533119202},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4698960483074188},{"id":"https://openalex.org/keywords/distributed-computing","display_name":"Distributed computing","score":0.3323413133621216},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.27872514724731445},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.21709251403808594},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.12843510508537292},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.07027828693389893},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.060146719217300415}],"concepts":[{"id":"https://openalex.org/C2779913896","wikidata":"https://www.wikidata.org/wiki/Q7063001","display_name":"Notice","level":2,"score":0.8200214505195618},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7572311758995056},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.6432428359985352},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.59397292137146},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5552802681922913},{"id":"https://openalex.org/C41550386","wikidata":"https://www.wikidata.org/wiki/Q529909","display_name":"Multi-agent system","level":2,"score":0.5387559533119202},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4698960483074188},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.3323413133621216},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.27872514724731445},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.21709251403808594},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.12843510508537292},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.07027828693389893},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.060146719217300415},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsi.2025.3539893","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2025.3539893","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"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 Circuits and Systems I: Regular Papers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3018282762","https://openalex.org/W2558055997","https://openalex.org/W2791183434","https://openalex.org/W1598820299","https://openalex.org/W2079049982","https://openalex.org/W1490949538","https://openalex.org/W2751205960","https://openalex.org/W2180200293","https://openalex.org/W2292721517","https://openalex.org/W2033417366"],"abstract_inverted_index":{"In":[0],"this":[1,83],"article,":[2],"we":[3,85],"deliver":[4],"analytical":[5,129],"expressions":[6,130],"to":[7,47,103],"characterize":[8],"the":[9,49,62,66,76,87,92,95,114,119,137,140,143,154],"attainable":[10],"consensusability":[11],"of":[12,78,94,118,131,142],"a":[13,35,39],"linear":[14],"unstable":[15,145],"multi-agent":[16],"system":[17],"(MAS).":[18],"The":[19],"considered":[20],"MAS":[21,120],"undergoes":[22],"uncertainty":[23],"variations":[24],"and":[25,65,97,128,150,158],"non-minimum":[26,147],"phase":[27,98,148,159],"dynamics,":[28],"whose":[29],"interaction":[30],"topology":[31],"is":[32,46],"delineated":[33],"by":[34],"communication":[36,59],"network":[37,60,151],"with":[38],"directed":[40],"spanning":[41],"tree.":[42],"Our":[43],"primary":[44],"objective":[45],"compute":[48],"maximal":[50],"robustness":[51,73,133],"consensus":[52,74,89,134,160],"margins,":[53,135],"which":[54,101],"can":[55],"clearly":[56],"describe":[57],"how":[58],"connectivity,":[61],"control":[63],"protocols,":[64],"system's":[67],"dynamics":[68],"exert":[69],"influences":[70],"on":[71,113,153],"allowable":[72],"in":[75],"framework":[77],"output":[79],"feedback":[80],"control.":[81],"Towards":[82],"aim,":[84],"resolve":[86],"robust":[88],"problem":[90],"along":[91],"spirit":[93],"gain":[96,157],"margin":[99],"problems,":[100],"amounts":[102],"handling":[104],"two":[105],"constrained":[106],"optimization":[107],"problems":[108],"over":[109],"feasible":[110],"regions":[111],"based":[112],"stability":[115],"analysis":[116],"theorem":[117],"characteristic":[121],"polynomials.":[122],"We":[123],"finally":[124],"formulate":[125],"explicit":[126],"conditions":[127],"achieved":[132,156],"wherein":[136],"results":[138],"show":[139],"restrictions":[141],"agent's":[144],"pole,":[146],"zero,":[149],"connectedness":[152],"robustly":[155],"margins.":[161]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
