{"id":"https://openalex.org/W4313889225","doi":"https://doi.org/10.3390/axioms12010065","title":"Robust Consensus in a Class of Fractional-Order Multi-Agent Systems with Interval Uncertainties Using the Existence Condition of Hermitian Matrices","display_name":"Robust Consensus in a Class of Fractional-Order Multi-Agent Systems with Interval Uncertainties Using the Existence Condition of Hermitian Matrices","publication_year":2023,"publication_date":"2023-01-07","ids":{"openalex":"https://openalex.org/W4313889225","doi":"https://doi.org/10.3390/axioms12010065"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12010065","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12010065","pdf_url":"https://www.mdpi.com/2075-1680/12/1/65/pdf?version=1674092168","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/1/65/pdf?version=1674092168","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041431502","display_name":"Mohammadreza Riazat","orcid":null},"institutions":[{"id":"https://openalex.org/I80543232","display_name":"K.N.Toosi University of Technology","ror":"https://ror.org/0433abe34","country_code":"IR","type":"education","lineage":["https://openalex.org/I80543232"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mohammadreza Riazat","raw_affiliation_strings":["Department of Electrical Engineering, K. N. Toosi University of Technology, Tehran 1631714191, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, K. N. Toosi University of Technology, Tehran 1631714191, Iran","institution_ids":["https://openalex.org/I80543232"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053903265","display_name":"Aydin Azizi","orcid":"https://orcid.org/0000-0001-6772-743X"},"institutions":[{"id":"https://openalex.org/I124261462","display_name":"Oxford Brookes University","ror":"https://ror.org/04v2twj65","country_code":"GB","type":"education","lineage":["https://openalex.org/I124261462"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Aydin Azizi","raw_affiliation_strings":["School of Engineering, Computing and Mathematics, Wheatley Campus, Oxford Brookes University, Oxford OX33 1HX, UK"],"raw_orcid":"https://orcid.org/0000-0001-6772-743X","affiliations":[{"raw_affiliation_string":"School of Engineering, Computing and Mathematics, Wheatley Campus, Oxford Brookes University, Oxford OX33 1HX, UK","institution_ids":["https://openalex.org/I124261462"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088655175","display_name":"Mojtaba Naderi Soorki","orcid":"https://orcid.org/0000-0001-6311-7220"},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mojtaba Naderi Soorki","raw_affiliation_strings":["Department of Electrical Engineering, Sharif University of Technology, Tehran 1458889694, Iran"],"raw_orcid":"https://orcid.org/0000-0001-6311-7220","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Sharif University of Technology, Tehran 1458889694, Iran","institution_ids":["https://openalex.org/I133529467"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083059964","display_name":"Abbasali Koochakzadeh","orcid":null},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Abbasali Koochakzadeh","raw_affiliation_strings":["Department of Electrical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran 1591634311, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran 1591634311, Iran","institution_ids":["https://openalex.org/I158248296"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5053903265"],"corresponding_institution_ids":["https://openalex.org/I124261462"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.5367,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.82836054,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"12","issue":"1","first_page":"65","last_page":"65"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":1.0,"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":1.0,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9980999827384949,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7692952752113342},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.6774254441261292},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5524519681930542},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5206879377365112},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4933566153049469},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.48793765902519226},{"id":"https://openalex.org/keywords/lyapunov-stability","display_name":"Lyapunov stability","score":0.4520284831523895},{"id":"https://openalex.org/keywords/stability-theory","display_name":"Stability theory","score":0.4485727548599243},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4415951669216156},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.4187544882297516},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3150770366191864},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.31443753838539124},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3116481900215149},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2019616663455963},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1925969123840332},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11399433016777039}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7692952752113342},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.6774254441261292},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5524519681930542},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5206879377365112},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4933566153049469},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.48793765902519226},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.4520284831523895},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.4485727548599243},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4415951669216156},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.4187544882297516},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3150770366191864},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31443753838539124},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3116481900215149},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2019616663455963},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1925969123840332},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11399433016777039},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12010065","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12010065","pdf_url":"https://www.mdpi.com/2075-1680/12/1/65/pdf?version=1674092168","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:523b69b74d9d4af08f809c135d1cec22","is_oa":true,"landing_page_url":"https://doaj.org/article/523b69b74d9d4af08f809c135d1cec22","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 1, p 65 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/1/65/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12010065","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 12; Issue 1; Pages: 65","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12010065","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12010065","pdf_url":"https://www.mdpi.com/2075-1680/12/1/65/pdf?version=1674092168","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.49000000953674316,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4313889225.pdf"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W331661423","https://openalex.org/W1535456175","https://openalex.org/W1987870286","https://openalex.org/W2024217322","https://openalex.org/W2030856696","https://openalex.org/W2039949070","https://openalex.org/W2047728847","https://openalex.org/W2086629900","https://openalex.org/W2125668987","https://openalex.org/W2156336948","https://openalex.org/W2166103243","https://openalex.org/W2168914013","https://openalex.org/W2171022983","https://openalex.org/W2477846956","https://openalex.org/W2790750964","https://openalex.org/W2970705789","https://openalex.org/W2984364074","https://openalex.org/W3000256825","https://openalex.org/W3012195570","https://openalex.org/W3041481232","https://openalex.org/W3157593080","https://openalex.org/W3163909249","https://openalex.org/W3167773925","https://openalex.org/W3169007562","https://openalex.org/W3186925220","https://openalex.org/W3199908702","https://openalex.org/W3209843899","https://openalex.org/W3217330375","https://openalex.org/W4200170779","https://openalex.org/W4220931132","https://openalex.org/W4293027867","https://openalex.org/W6795513590","https://openalex.org/W6796435000"],"related_works":["https://openalex.org/W2009168760","https://openalex.org/W1495650726","https://openalex.org/W2210722882","https://openalex.org/W2041491087","https://openalex.org/W2963043651","https://openalex.org/W2057820893","https://openalex.org/W2106591639","https://openalex.org/W2383820201","https://openalex.org/W2534107666","https://openalex.org/W170012745"],"abstract_inverted_index":{"This":[0,89],"study":[1],"outlines":[2],"the":[3,45,57,85,94,98,133,137,140,170,182,191,195,199,229,240,243],"necessary":[4,171],"and":[5,34,50,65,130,172],"sufficient":[6,173],"criteria":[7],"for":[8,25,82],"swarm":[9],"stability":[10],"asymptotically,":[11],"meaning":[12],"consensus":[13,63,177],"in":[14,101,178,181,217],"a":[15,75,102,116,128,131,148,160,168,179,207,226],"class":[16],"of":[17,78,84,97,139,143,147,163,184,198,203,210,228,242],"fractional-order":[18,58],"multi-agent":[19,60,117],"systems":[20],"(FOMAS)":[21],"with":[22,119],"interval":[23,59],"uncertainties":[24,186],"both":[26],"fractional":[27],"orders":[28],"0":[29],"&lt;":[30,32,36,38],"\u03b1":[31,37],"1":[33,35],"2.":[39],"The":[40],"constraints":[41],"are":[42,69,187,236],"determined":[43],"by":[44,92,157],"graph":[46],"topology,":[47],"agent":[48],"dynamics,":[49],"neighbor":[51],"interactions.":[52],"It":[53],"is":[54,90,111,150],"demonstrated":[55],"that":[56,73],"system":[61,86,118,164],"achieves":[62],"if":[64,67],"only":[66,159,206],"there":[68],"some":[70,154,222,231],"Hermitian":[71,99,155,223],"matrices":[72,100,156,212],"satisfy":[74],"particular":[76],"kind":[77],"complex":[79],"Lyapunov":[80,103,134,192,218],"inequality":[81,135],"all":[83],"vertex":[87,165,211],"matrices.":[88,166,224],"done":[91],"using":[93,127],"existence":[95],"condition":[96],"inequality.":[104],"To":[105],"do":[106],"this,":[107],"at":[108,239],"first":[109],"it":[110],"shown":[112],"under":[113],"which":[114],"conditions":[115,174],"unstable":[120],"agents":[121],"can":[122],"still":[123],"achieve":[124],"consensus.":[125],"Then,":[126],"lemma":[129],"theory,":[132],"regarding":[136],"negativity":[138],"maximum":[141],"eigenvalue":[142],"an":[144],"augmented":[145],"matrix":[146],"FOMAS":[149,180],"used":[151,216],"to":[152,175,190,214,220],"find":[153,221],"checking":[158],"limited":[161,208],"number":[162,209],"As":[167,225],"result,":[169],"reach":[176],"presence":[183],"internal":[185],"obtained":[188],"according":[189],"inequalities.":[193],"Using":[194],"main":[196],"theory":[197],"current":[200],"paper,":[201],"instead":[202],"countless":[204],"matrices,":[205],"need":[213],"be":[215],"inequalities":[219],"confirmation":[227],"notion,":[230],"instances":[232],"from":[233],"numerical":[234],"simulation":[235],"also":[237],"provided":[238],"end":[241],"paper.":[244]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2023-01-10T00:00:00"}
