{"id":"https://openalex.org/W2121116776","doi":"https://doi.org/10.1109/cdc.2009.5400537","title":"Distributed discrete-time nonlinear consensus protocols","display_name":"Distributed discrete-time nonlinear consensus protocols","publication_year":2009,"publication_date":"2009-12-01","ids":{"openalex":"https://openalex.org/W2121116776","doi":"https://doi.org/10.1109/cdc.2009.5400537","mag":"2121116776"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2009.5400537","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2009.5400537","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference","raw_type":"proceedings-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/A5001092290","display_name":"Jing Zhou","orcid":"https://orcid.org/0000-0003-1676-5991"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jing Zhou","raw_affiliation_strings":["Mechanical Engineering, Pennsylvania State University, University Park, PA, USA","Mechanical Engineering, Penn State University, University Park, 16802, USA"],"affiliations":[{"raw_affiliation_string":"Mechanical Engineering, Pennsylvania State University, University Park, PA, USA","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Mechanical Engineering, Penn State University, University Park, 16802, USA","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100391004","display_name":"Qian Wang","orcid":"https://orcid.org/0000-0001-7175-2777"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qian Wang","raw_affiliation_strings":["Mechanical Engineering, Pennsylvania State University, University Park, PA, USA","Mechanical Engineering, Penn State University, University Park, 16802, USA"],"affiliations":[{"raw_affiliation_string":"Mechanical Engineering, Pennsylvania State University, University Park, PA, USA","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Mechanical Engineering, Penn State University, University Park, 16802, USA","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001092290"],"corresponding_institution_ids":["https://openalex.org/I130769515"],"apc_list":null,"apc_paid":null,"fwci":0.3428,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.64024195,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"44","issue":null,"first_page":"4759","last_page":"4764"},"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":0.9994000196456909,"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/T10080","display_name":"Energy Efficient Wireless Sensor Networks","score":0.9904000163078308,"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/convergence","display_name":"Convergence (economics)","score":0.7253844738006592},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6807498931884766},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6141095161437988},{"id":"https://openalex.org/keywords/consensus","display_name":"Consensus","score":0.554707944393158},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.5466237664222717},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.5247880816459656},{"id":"https://openalex.org/keywords/uniform-consensus","display_name":"Uniform consensus","score":0.510303258895874},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5007071495056152},{"id":"https://openalex.org/keywords/exponential-growth","display_name":"Exponential growth","score":0.4822124242782593},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4576420485973358},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4082731008529663},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.401334673166275},{"id":"https://openalex.org/keywords/multi-agent-system","display_name":"Multi-agent system","score":0.38730692863464355},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37030214071273804},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3271869421005249},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11436071991920471},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10046270489692688},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.07729554176330566},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07717680931091309}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7253844738006592},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6807498931884766},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6141095161437988},{"id":"https://openalex.org/C107107730","wikidata":"https://www.wikidata.org/wiki/Q2994424","display_name":"Consensus","level":3,"score":0.554707944393158},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.5466237664222717},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.5247880816459656},{"id":"https://openalex.org/C80966040","wikidata":"https://www.wikidata.org/wiki/Q7885028","display_name":"Uniform consensus","level":4,"score":0.510303258895874},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5007071495056152},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.4822124242782593},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4576420485973358},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4082731008529663},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.401334673166275},{"id":"https://openalex.org/C41550386","wikidata":"https://www.wikidata.org/wiki/Q529909","display_name":"Multi-agent system","level":2,"score":0.38730692863464355},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37030214071273804},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3271869421005249},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11436071991920471},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10046270489692688},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.07729554176330566},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07717680931091309},{"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/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},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2009.5400537","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2009.5400537","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.44999998807907104,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1499871105","https://openalex.org/W1864806140","https://openalex.org/W1964647857","https://openalex.org/W2007696489","https://openalex.org/W2050361638","https://openalex.org/W2074796812","https://openalex.org/W2083644756","https://openalex.org/W2099175737","https://openalex.org/W2107396783","https://openalex.org/W2110530726","https://openalex.org/W2111366290","https://openalex.org/W2115428923","https://openalex.org/W2122093006","https://openalex.org/W2125668987","https://openalex.org/W2135097535","https://openalex.org/W2146890818","https://openalex.org/W2154693758","https://openalex.org/W2165744313","https://openalex.org/W2167677395","https://openalex.org/W2172498959","https://openalex.org/W4247555059","https://openalex.org/W6657899995","https://openalex.org/W6685402832"],"related_works":["https://openalex.org/W2017057923","https://openalex.org/W2017013062","https://openalex.org/W2118264468","https://openalex.org/W2021821379","https://openalex.org/W2335243741","https://openalex.org/W2781671274","https://openalex.org/W2032218247","https://openalex.org/W2002561675","https://openalex.org/W3012103079","https://openalex.org/W2159384302"],"abstract_inverted_index":{"In":[0,34,87],"this":[1],"paper,":[2],"we":[3,46],"study":[4],"the":[5,20,42,52,88],"discrete-time":[6,54],"nonlinear":[7,56],"consensus":[8,38,57,72],"protocols":[9,58],"over":[10,59],"both":[11],"directed":[12],"and":[13],"undirected":[14],"networks":[15],"with":[16,29],"fixed":[17],"topology.":[18],"First,":[19],"notions":[21],"of":[22,32,36,44,83],"(global/exponential)":[23,37],"semistability":[24],"are":[25],"introduced":[26],"for":[27,51],"systems":[28],"a":[30,90],"continuum":[31],"equilibria.":[33],"terms":[35],"defined":[39],"based":[40],"on":[41,70],"notion":[43],"semistability,":[45],"have":[47],"derived":[48,79],"convergence":[49,68],"conditions":[50],"general":[53],"distributed":[55],"directed/undirected":[60],"weighted":[61],"networks.":[62],"We":[63],"also":[64],"show":[65],"that":[66],"several":[67],"results":[69],"linear":[71],"problems":[73],"in":[74],"existing":[75],"literature":[76],"can":[77],"be":[78],"as":[80],"special":[81],"cases":[82],"our":[84,97],"main":[85],"result.":[86],"end,":[89],"numerical":[91],"example":[92],"is":[93],"given":[94],"to":[95],"illustrate":[96],"theoretical":[98],"results.":[99]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}