{"id":"https://openalex.org/W2912171307","doi":"https://doi.org/10.1109/tac.2019.2910948","title":"Lyapunov Criterion for Stochastic Systems and Its Applications in Distributed Computation","display_name":"Lyapunov Criterion for Stochastic Systems and Its Applications in Distributed Computation","publication_year":2019,"publication_date":"2019-05-21","ids":{"openalex":"https://openalex.org/W2912171307","doi":"https://doi.org/10.1109/tac.2019.2910948","mag":"2912171307"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2019.2910948","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2019.2910948","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.rug.nl/en/publications/7c5902e7-ae2f-4de0-a69d-826867cb1e42","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003846639","display_name":"Yuzhen Qin","orcid":"https://orcid.org/0000-0003-1851-1370"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Yuzhen Qin","raw_affiliation_strings":["Institute of Engineering and Technology, Faculty of Science and Engineering, University of Groningen, Groningen, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Institute of Engineering and Technology, Faculty of Science and Engineering, University of Groningen, Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021403340","display_name":"Ming Cao","orcid":"https://orcid.org/0000-0001-5472-562X"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Ming Cao","raw_affiliation_strings":["Institute of Engineering and Technology, Faculty of Science and Engineering, University of Groningen, Groningen, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Institute of Engineering and Technology, Faculty of Science and Engineering, University of Groningen, Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015736743","display_name":"Brian D. O. Anderson","orcid":"https://orcid.org/0000-0002-1493-4774"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]},{"id":"https://openalex.org/I1292875679","display_name":"Commonwealth Scientific and Industrial Research Organisation","ror":"https://ror.org/03qn8fb07","country_code":"AU","type":"government","lineage":["https://openalex.org/I1292875679","https://openalex.org/I2801453606","https://openalex.org/I4387156119"]},{"id":"https://openalex.org/I42894916","display_name":"Data61","ror":"https://ror.org/03q397159","country_code":"AU","type":"other","lineage":["https://openalex.org/I1292875679","https://openalex.org/I2801453606","https://openalex.org/I42894916","https://openalex.org/I4387156119"]},{"id":"https://openalex.org/I50760025","display_name":"Hangzhou Dianzi University","ror":"https://ror.org/0576gt767","country_code":"CN","type":"education","lineage":["https://openalex.org/I50760025"]}],"countries":["AU","CN"],"is_corresponding":false,"raw_author_name":"Brian D. O. Anderson","raw_affiliation_strings":["Data61-CSIRO, Canberra, Australia","Research School of Electrical, Energy and Materials Engineering, Australian National University, Canberra, Australia","School of Automation, Hangzhou Dianzi University, Hangzhou, China"],"affiliations":[{"raw_affiliation_string":"Data61-CSIRO, Canberra, Australia","institution_ids":["https://openalex.org/I42894916","https://openalex.org/I1292875679"]},{"raw_affiliation_string":"Research School of Electrical, Energy and Materials Engineering, Australian National University, Canberra, Australia","institution_ids":["https://openalex.org/I118347636"]},{"raw_affiliation_string":"School of Automation, Hangzhou Dianzi University, Hangzhou, China","institution_ids":["https://openalex.org/I50760025"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5003846639"],"corresponding_institution_ids":["https://openalex.org/I169381384"],"apc_list":null,"apc_paid":null,"fwci":3.8929,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.94005393,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"65","issue":"2","first_page":"546","last_page":"560"},"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":0.9991000294685364,"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/T10080","display_name":"Energy Efficient Wireless Sensor Networks","score":0.9944000244140625,"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/lyapunov-function","display_name":"Lyapunov function","score":0.7441471815109253},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6848406791687012},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5536346435546875},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.542091429233551},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5290821194648743},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4808272123336792},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4505605101585388},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.43224266171455383},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.430997759103775},{"id":"https://openalex.org/keywords/diagonal-matrix","display_name":"Diagonal matrix","score":0.41637179255485535},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2011718451976776},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19192466139793396},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.15549978613853455},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.08832678198814392}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7441471815109253},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6848406791687012},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5536346435546875},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.542091429233551},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5290821194648743},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4808272123336792},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4505605101585388},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.43224266171455383},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.430997759103775},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.41637179255485535},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2011718451976776},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19192466139793396},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.15549978613853455},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.08832678198814392},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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":4,"locations":[{"id":"doi:10.1109/tac.2019.2910948","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2019.2910948","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:pure.rug.nl:openaire/7c5902e7-ae2f-4de0-a69d-826867cb1e42","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/7c5902e7-ae2f-4de0-a69d-826867cb1e42","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Qin, Y, Cao, M & Anderson, B D O 2020, 'Lyapunov Criterion for Stochastic Systems and Its Applications in Distributed Computation', IEEE-Transactions on Automatic Control, vol. 65, no. 2, 8691522, pp. 546-560. https://doi.org/10.1109/TAC.2019.2910948","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1902.04332","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1902.04332","pdf_url":"https://arxiv.org/pdf/1902.04332","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:openresearch-repository.anu.edu.au:1885/227135","is_oa":false,"landing_page_url":"http://hdl.handle.net/1885/227135","pdf_url":null,"source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"Journal article"}],"best_oa_location":{"id":"pmh:oai:pure.rug.nl:openaire/7c5902e7-ae2f-4de0-a69d-826867cb1e42","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/7c5902e7-ae2f-4de0-a69d-826867cb1e42","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Qin, Y, Cao, M & Anderson, B D O 2020, 'Lyapunov Criterion for Stochastic Systems and Its Applications in Distributed Computation', IEEE-Transactions on Automatic Control, vol. 65, no. 2, 8691522, pp. 546-560. https://doi.org/10.1109/TAC.2019.2910948","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1469968259","display_name":null,"funder_award_id":"NWO-vidi-14134","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G5365867299","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G6351849200","display_name":null,"funder_award_id":"DP-160104500","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G6403596008","display_name":null,"funder_award_id":"ERC-CoG-771687","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G6765546875","display_name":null,"funder_award_id":"160104500","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G826542851","display_name":null,"funder_award_id":"DP-130103610","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G8487148130","display_name":null,"funder_award_id":"Data61-CSIRO","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320320386","display_name":"Commonwealth Scientific and Industrial Research Organisation","ror":"https://ror.org/03qn8fb07"},{"id":"https://openalex.org/F4320320933","display_name":"Rijksuniversiteit Groningen","ror":"https://ror.org/012p63287"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W199736301","https://openalex.org/W1489872560","https://openalex.org/W1579485993","https://openalex.org/W1603765807","https://openalex.org/W1769473688","https://openalex.org/W1964647857","https://openalex.org/W1976631094","https://openalex.org/W1985049996","https://openalex.org/W1985813210","https://openalex.org/W1995313864","https://openalex.org/W1998067439","https://openalex.org/W2009668633","https://openalex.org/W2019312235","https://openalex.org/W2035039048","https://openalex.org/W2044212084","https://openalex.org/W2053642888","https://openalex.org/W2054312097","https://openalex.org/W2056356355","https://openalex.org/W2060853821","https://openalex.org/W2064770819","https://openalex.org/W2073460177","https://openalex.org/W2101051269","https://openalex.org/W2103554135","https://openalex.org/W2112891556","https://openalex.org/W2114403255","https://openalex.org/W2122093006","https://openalex.org/W2134591574","https://openalex.org/W2137435346","https://openalex.org/W2144408773","https://openalex.org/W2154834860","https://openalex.org/W2160413708","https://openalex.org/W2261343011","https://openalex.org/W2295171903","https://openalex.org/W2406068819","https://openalex.org/W2409095450","https://openalex.org/W2567931453","https://openalex.org/W2569714389","https://openalex.org/W2576544140","https://openalex.org/W2584178556","https://openalex.org/W2623327125","https://openalex.org/W2785076823","https://openalex.org/W2898740902","https://openalex.org/W2963156126","https://openalex.org/W3099660372","https://openalex.org/W4231144031","https://openalex.org/W4232753567","https://openalex.org/W4242086383","https://openalex.org/W4244300861","https://openalex.org/W4297744580","https://openalex.org/W4300588288","https://openalex.org/W4301121837","https://openalex.org/W4301885439","https://openalex.org/W6747963927"],"related_works":["https://openalex.org/W2107786365","https://openalex.org/W1529195008","https://openalex.org/W2034395027","https://openalex.org/W2028994362","https://openalex.org/W38983538","https://openalex.org/W2924468784","https://openalex.org/W2034598826","https://openalex.org/W4285317199","https://openalex.org/W2087913063","https://openalex.org/W1525824672"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"new":[3,60],"sufficient":[4,83],"conditions":[5,84,130],"for":[6,122],"convergence":[7,105],"and":[8,81],"asymptotic":[9],"or":[10],"exponential":[11,108],"stability":[12],"of":[13,36,58,68,72,104],"a":[14,33,93,118],"stochastic":[15,51,73],"discrete-time":[16],"system,":[17],"under":[18,109],"which":[19],"the":[20,29,49,55,66,87,102,113,132,138],"constructed":[21],"Lyapunov":[22,52,61],"function":[23],"always":[24],"decreases":[25],"in":[26,46],"expectation":[27],"along":[28],"system's":[30],"solutions":[31],"after":[32],"finite":[34],"number":[35],"steps,":[37],"but":[38],"without":[39],"necessarily":[40],"strict":[41],"decrease":[42],"at":[43,65],"every":[44],"step,":[45],"contrast":[47],"to":[48,85,92],"classical":[50],"theory.":[53],"As":[54,112],"first":[56],"application":[57],"this":[59],"criterion,":[62],"we":[63,98,116],"look":[64],"product":[67,88],"any":[69],"random":[70],"sequence":[71],"matrices,":[74],"including":[75],"those":[76],"with":[77,95],"zero":[78],"diagonal":[79],"entries,":[80],"obtain":[82],"ensure":[86],"almost":[89],"surely":[90],"converges":[91],"matrix":[94],"identical":[96],"rows;":[97],"also":[99],"show":[100],"that":[101],"rate":[103],"can":[106],"be":[107],"additional":[110],"conditions.":[111],"second":[114],"application,":[115],"study":[117],"distributed":[119],"network":[120,133],"algorithm":[121],"solving":[123],"linear":[124],"algebraic":[125],"equations.":[126],"We":[127],"relax":[128],"existing":[129],"on":[131],"structures,":[134],"while":[135],"still":[136],"guaranteeing":[137],"equations":[139],"are":[140],"solved":[141],"asymptotically.":[142]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
