{"id":"https://openalex.org/W2100607192","doi":"https://doi.org/10.1109/acc.2003.1240542","title":"Complete characterization of quadratic Lyapunov functions for planar systems in LMI regions","display_name":"Complete characterization of quadratic Lyapunov functions for planar systems in LMI regions","publication_year":2004,"publication_date":"2004-01-23","ids":{"openalex":"https://openalex.org/W2100607192","doi":"https://doi.org/10.1109/acc.2003.1240542","mag":"2100607192"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2003.1240542","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2003.1240542","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2003 American Control Conference, 2003.","raw_type":"proceedings-article"},"type":"conference-paper","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/A5100651224","display_name":"Dongmei Xie","orcid":null},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dongmei Xie","raw_affiliation_strings":["Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing, China","[Dept. of Mech. & Eng. Sci., Peking Univ., Beijing, China]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"[Dept. of Mech. & Eng. Sci., Peking Univ., Beijing, China]","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100447536","display_name":"Long Wang","orcid":"https://orcid.org/0000-0001-5600-8157"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Long Wang","raw_affiliation_strings":["Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing, China","[Dept. of Mech. & Eng. Sci., Peking Univ., Beijing, China]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"[Dept. of Mech. & Eng. Sci., Peking Univ., Beijing, China]","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044920558","display_name":"Guangming Xie","orcid":"https://orcid.org/0000-0001-6504-0087"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guangming Xie","raw_affiliation_strings":["Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing, China","[Dept. of Mech. & Eng. Sci., Peking Univ., Beijing, China]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"[Dept. of Mech. & Eng. Sci., Peking Univ., Beijing, China]","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I20231570"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16686073,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"5","issue":null,"first_page":"4457","last_page":"4462"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.7396957278251648},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6703101396560669},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6556747555732727},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.649720311164856},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6377361416816711},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.6290427446365356},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4867987334728241},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4536338746547699},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4103812575340271},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2864760160446167},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2607218623161316},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.18225204944610596},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09639689326286316},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.058585941791534424}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7396957278251648},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6703101396560669},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6556747555732727},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.649720311164856},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6377361416816711},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.6290427446365356},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4867987334728241},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4536338746547699},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4103812575340271},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2864760160446167},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2607218623161316},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.18225204944610596},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09639689326286316},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.058585941791534424},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","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/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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2003.1240542","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2003.1240542","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2003 American Control Conference, 2003.","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1547135986","https://openalex.org/W1972848510","https://openalex.org/W1973506044","https://openalex.org/W2104901372","https://openalex.org/W2171222770","https://openalex.org/W4235661195"],"related_works":["https://openalex.org/W4311883357","https://openalex.org/W2377770720","https://openalex.org/W2113626999","https://openalex.org/W160889949","https://openalex.org/W2364696089","https://openalex.org/W309910862","https://openalex.org/W4210637712","https://openalex.org/W2369004811","https://openalex.org/W2392500469","https://openalex.org/W3195956009"],"abstract_inverted_index":{"This":[0],"paper":[1,27],"discusses":[2],"the":[3,70],"problem":[4],"of":[5,25,34,62],"finding":[6],"a":[7,31,40,53,60,67],"common":[8],"quadratic":[9,35],"Lyapunov":[10,36],"function":[11],"(CQLF)":[12],"for":[13,39,58],"planar":[14,42,63],"systems":[15,64],"in":[16,47,69],"linear":[17],"matrix":[18],"inequality":[19],"(LMI)":[20],"regions.":[21],"The":[22,73],"main":[23],"contribution":[24],"this":[26],"is":[28,45],"to":[29,65],"give":[30],"complete":[32],"characterization":[33],"functions":[37],"(QLFs)":[38],"given":[41],"system,":[43],"which":[44,82],"stable":[46],"an":[48],"LMI":[49,71],"region,":[50],"and":[51,55],"obtain":[52],"necessary":[54],"sufficient":[56],"condition":[57],"such":[59],"class":[61],"share":[66],"CQLF":[68],"region.":[72],"results":[74],"are":[75],"not":[76],"only":[77],"verifiable":[78],"but":[79],"also":[80],"constructive,":[81],"can":[83],"be":[84],"realized":[85],"by":[86],"computer":[87],"easily.":[88]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
