{"id":"https://openalex.org/W2030220106","doi":"https://doi.org/10.1137/100816870","title":"Convergence Results for the Linear Consensus Problem under Markovian Random Graphs","display_name":"Convergence Results for the Linear Consensus Problem under Markovian Random Graphs","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2030220106","doi":"https://doi.org/10.1137/100816870","mag":"2030220106"},"language":"en","primary_location":{"id":"doi:10.1137/100816870","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100816870","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5031818939","display_name":"Ion Matei","orcid":"https://orcid.org/0000-0001-5555-8130"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ion Matei","raw_affiliation_strings":["Institute for Systems Research, University of Maryland, College Park, MD 20742"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Systems Research, University of Maryland, College Park, MD 20742","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044395526","display_name":"John S. Baras","orcid":"https://orcid.org/0000-0002-4955-8561"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John S. Baras","raw_affiliation_strings":["Institute for Systems Research, University of Maryland, College Park, MD 20742"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Systems Research, University of Maryland, College Park, MD 20742","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080167889","display_name":"Christoforos Somarakis","orcid":"https://orcid.org/0000-0003-4601-2501"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christoforos Somarakis","raw_affiliation_strings":["Institute for Systems Research, University of Maryland, College Park, MD 20742"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Systems Research, University of Maryland, College Park, MD 20742","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I66946132"],"apc_list":null,"apc_paid":null,"fwci":16.0328,"has_fulltext":false,"cited_by_count":112,"citation_normalized_percentile":{"value":0.99066651,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"51","issue":"2","first_page":"1574","last_page":"1591"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9998999834060669,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.989799976348877,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9757999777793884,"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/mathematics","display_name":"Mathematics","score":0.7434609532356262},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.6326056122779846},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5782807469367981},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5451840162277222},{"id":"https://openalex.org/keywords/jump-process","display_name":"Jump process","score":0.5294570326805115},{"id":"https://openalex.org/keywords/consensus","display_name":"Consensus","score":0.5089929103851318},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.45849835872650146},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.45747989416122437},{"id":"https://openalex.org/keywords/strongly-connected-component","display_name":"Strongly connected component","score":0.44581910967826843},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.43241071701049805},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.42979395389556885},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.42930880188941956},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.39151501655578613},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38574835658073425},{"id":"https://openalex.org/keywords/multi-agent-system","display_name":"Multi-agent system","score":0.2352946698665619},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19078558683395386}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7434609532356262},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.6326056122779846},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5782807469367981},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5451840162277222},{"id":"https://openalex.org/C2776825372","wikidata":"https://www.wikidata.org/wiki/Q3922411","display_name":"Jump process","level":3,"score":0.5294570326805115},{"id":"https://openalex.org/C107107730","wikidata":"https://www.wikidata.org/wiki/Q2994424","display_name":"Consensus","level":3,"score":0.5089929103851318},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.45849835872650146},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45747989416122437},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.44581910967826843},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.43241071701049805},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.42979395389556885},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.42930880188941956},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.39151501655578613},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38574835658073425},{"id":"https://openalex.org/C41550386","wikidata":"https://www.wikidata.org/wiki/Q529909","display_name":"Multi-agent system","level":2,"score":0.2352946698665619},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19078558683395386},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/100816870","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100816870","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.386.6157","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.386.6157","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ece.umd.edu/~baras/publications/journals/2013-SIAM-matei_baras_somar-convergence_consensus_markovian_random_graphs.pdf","raw_type":"text"},{"id":"pmh:oai:drum.lib.umd.edu:1903/9693","is_oa":false,"landing_page_url":"http://hdl.handle.net/1903/9693","pdf_url":null,"source":{"id":"https://openalex.org/S4306401518","display_name":"University Libraries (University of Maryland)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66946132","host_organization_name":"University of Maryland, College Park","host_organization_lineage":["https://openalex.org/I66946132"],"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":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1093939616","display_name":null,"funder_award_id":"CNS-1035655","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G1560897552","display_name":null,"funder_award_id":"FA9550-09-1-0538","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G3622582212","display_name":null,"funder_award_id":"W911NF-08-1","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G483727992","display_name":null,"funder_award_id":"W911NF-08-1-0238","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"},{"id":"https://openalex.org/G4988052250","display_name":null,"funder_award_id":"W911NF-08-1-0238","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G6014290904","display_name":"CPS: Large: Science of Integration for Cyber-Physical Systems","funder_award_id":"1035655","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6904062931","display_name":null,"funder_award_id":"FA9550-09-1-0538","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1490978409","https://openalex.org/W1528184823","https://openalex.org/W1547358136","https://openalex.org/W1864806140","https://openalex.org/W1964647857","https://openalex.org/W1976625337","https://openalex.org/W1984661256","https://openalex.org/W2020857459","https://openalex.org/W2032803680","https://openalex.org/W2044212084","https://openalex.org/W2093777540","https://openalex.org/W2099175737","https://openalex.org/W2101641320","https://openalex.org/W2107396783","https://openalex.org/W2114403255","https://openalex.org/W2114791779","https://openalex.org/W2115428923","https://openalex.org/W2125668987","https://openalex.org/W2145706050","https://openalex.org/W2154834860","https://openalex.org/W2160413708","https://openalex.org/W2160643434","https://openalex.org/W2161935574","https://openalex.org/W2165744313","https://openalex.org/W4247555059"],"related_works":["https://openalex.org/W2000908595","https://openalex.org/W2601620533","https://openalex.org/W2665822041","https://openalex.org/W2058185550","https://openalex.org/W2980902902","https://openalex.org/W1979834611","https://openalex.org/W2938096743","https://openalex.org/W2086661292","https://openalex.org/W4388579762","https://openalex.org/W2020674965"],"abstract_inverted_index":{"This":[0],"paper":[1,114],"discusses":[2],"the":[3,41,45,48,51,67,78,83,91,95,101,104,121],"linear":[4,126],"asymptotic":[5],"consensus":[6,68,74,147],"problem":[7],"for":[8,145],"a":[9,20,29,38],"network":[10,16],"of":[11,40,50,97,103,112,123],"dynamic":[12],"agents":[13,52],"whose":[14],"communication":[15],"is":[17,26,53,75,107,115],"modeled":[18],"by":[19,28,133],"randomly":[21],"switching":[22,25],"graph.":[23],"The":[24,110],"determined":[27],"finite":[30],"state":[31,39],"Markov":[32,105],"process,":[33],"each":[34],"topology":[35],"corresponding":[36,99],"to":[37,100,116,141],"process.":[42],"We":[43,63],"address":[44],"cases":[46],"where":[47],"dynamics":[49],"expressed":[54],"both":[55],"in":[56,60,77,128],"continuous":[57],"time":[58],"and":[59,82,88,135],"discrete":[61],"time.":[62],"show":[64,117],"that,":[65],"if":[66,87,90],"matrices":[69],"are":[70],"doubly":[71],"stochastic,":[72],"average":[73],"achieved":[76],"mean":[79],"square":[80],"sense":[81,86],"almost":[84],"sure":[85],"only":[89],"graph":[92,136],"resulting":[93],"from":[94,120],"union":[96],"graphs":[98],"states":[102],"process":[106],"strongly":[108],"connected.":[109],"aim":[111],"this":[113],"how":[118],"techniques":[119],"theory":[122],"Markovian":[124],"jump":[125],"systems,":[127],"conjunction":[129],"with":[130],"results":[131,144],"inspired":[132],"matrix":[134],"theory,":[137],"can":[138],"be":[139],"used":[140],"prove":[142],"convergence":[143],"stochastic":[146],"problems.":[148]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":14},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":5}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
