{"id":"https://openalex.org/W2002429047","doi":"https://doi.org/10.1142/s0218127409022932","title":"A LIE ALGEBRAIC CONDITION OF STABILITY FOR HYBRID SYSTEMS AND APPLICATION TO HYBRID SYNCHRONIZATION","display_name":"A LIE ALGEBRAIC CONDITION OF STABILITY FOR HYBRID SYSTEMS AND APPLICATION TO HYBRID SYNCHRONIZATION","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2002429047","doi":"https://doi.org/10.1142/s0218127409022932","mag":"2002429047"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127409022932","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127409022932","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5101841046","display_name":"Shouwei Zhao","orcid":"https://orcid.org/0000-0003-4762-8850"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"SHOUWEI ZHAO","raw_affiliation_strings":["Department of Mathematics, Tongji University, Shanghai 200092, P. R. China","Department of Mathematics , Tongji University , Shanghai, 200092 , P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Tongji University, Shanghai 200092, P. R. China","institution_ids":["https://openalex.org/I116953780"]},{"raw_affiliation_string":"Department of Mathematics , Tongji University , Shanghai, 200092 , P.R. China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049902919","display_name":"Jitao Sun","orcid":"https://orcid.org/0000-0002-9581-8336"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"JITAO SUN","raw_affiliation_strings":["Department of Mathematics, Tongji University, Shanghai 200092, P. R. China","Department of Mathematics , Tongji University , Shanghai, 200092 , P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Tongji University, Shanghai 200092, P. R. China","institution_ids":["https://openalex.org/I116953780"]},{"raw_affiliation_string":"Department of Mathematics , Tongji University , Shanghai, 200092 , P.R. China","institution_ids":["https://openalex.org/I116953780"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I116953780"],"apc_list":null,"apc_paid":null,"fwci":0.7101,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.69979322,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"19","issue":"01","first_page":"379","last_page":"386"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9983000159263611,"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/lie-algebra","display_name":"Lie algebra","score":0.7395694255828857},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.684291422367096},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.6334826350212097},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6025543212890625},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5786288380622864},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.542910635471344},{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.45419883728027344},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4520421624183655},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.43219539523124695},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41678041219711304},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.35059159994125366},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32663780450820923},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.23754000663757324},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18515193462371826},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15983039140701294},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.12879565358161926},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07990959286689758}],"concepts":[{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.7395694255828857},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.684291422367096},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.6334826350212097},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6025543212890625},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5786288380622864},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.542910635471344},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.45419883728027344},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4520421624183655},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.43219539523124695},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41678041219711304},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35059159994125366},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32663780450820923},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.23754000663757324},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18515193462371826},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15983039140701294},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.12879565358161926},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07990959286689758},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127409022932","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127409022932","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1499154045","https://openalex.org/W1517768962","https://openalex.org/W1969661013","https://openalex.org/W1995454290","https://openalex.org/W2009925075","https://openalex.org/W2011373950","https://openalex.org/W2013142479","https://openalex.org/W2021847233","https://openalex.org/W2028712742","https://openalex.org/W2060546335","https://openalex.org/W2067402505","https://openalex.org/W2077402293","https://openalex.org/W2106566376","https://openalex.org/W2113789361","https://openalex.org/W2119384322","https://openalex.org/W2120723458","https://openalex.org/W2143181390","https://openalex.org/W2157114154","https://openalex.org/W3099639122"],"related_works":["https://openalex.org/W1593898832","https://openalex.org/W2142048021","https://openalex.org/W2756324413","https://openalex.org/W2380573388","https://openalex.org/W2383529437","https://openalex.org/W2134075948","https://openalex.org/W2963288691","https://openalex.org/W4298401637","https://openalex.org/W2940979654","https://openalex.org/W2105339944"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,42],"first":[4],"present":[5],"a":[6,22,44,58,70,75],"Lie":[7,23,65],"algebraic":[8],"condition":[9,61],"for":[10,47,69],"global":[11,48],"exponential":[12,49],"stability":[13,50],"of":[14,36,51,64],"linear":[15,52],"switched":[16,53,77],"and":[17,30,54,78],"impulsive":[18,31,55,79],"systems.":[19,56],"By":[20],"considering":[21],"algebra":[24,66],"generated":[25],"by":[26,90],"all":[27,35],"subsystem":[28],"matrices":[29,38],"matrices,":[32],"when":[33],"not":[34],"these":[37],"are":[39],"Hurwitz/Schur":[40],"stable":[41],"derive":[43],"new":[45],"criterion":[46],"Then":[57],"simple":[59],"sufficient":[60],"in":[62],"terms":[63],"is":[67,88],"established":[68],"nonlinear":[71],"system":[72],"synchronization":[73,87,94],"using":[74],"hybrid":[76],"control.":[80],"As":[81],"an":[82],"application,":[83],"Chua's":[84],"chaotic":[85],"circuit's":[86],"investigated":[89],"our":[91],"method":[92],"while":[93],"cannot":[95],"be":[96],"achieved":[97],"with":[98],"the":[99],"existing":[100],"result.":[101]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
