{"id":"https://openalex.org/W1974855544","doi":"https://doi.org/10.1109/tcsii.2012.2200172","title":"Lyapunov-Type Theorem of General Two-Dimensional Nonlinear Parameter-Varying FM Second Model","display_name":"Lyapunov-Type Theorem of General Two-Dimensional Nonlinear Parameter-Varying FM Second Model","publication_year":2012,"publication_date":"2012-05-31","ids":{"openalex":"https://openalex.org/W1974855544","doi":"https://doi.org/10.1109/tcsii.2012.2200172","mag":"1974855544"},"language":"en","primary_location":{"id":"doi:10.1109/tcsii.2012.2200172","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsii.2012.2200172","pdf_url":null,"source":{"id":"https://openalex.org/S93916849","display_name":"IEEE Transactions on Circuits & Systems II Express Briefs","issn_l":"1549-7747","issn":["1549-7747","1558-3791"],"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 Circuits and Systems II: Express Briefs","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/A5103145997","display_name":"Qiao Zhu","orcid":"https://orcid.org/0000-0002-6200-6657"},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiao Zhu","raw_affiliation_strings":["School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China","Sch. of Autom. & Electr. Eng, Univ. of Sci. & Technol. Beijing, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China","institution_ids":["https://openalex.org/I92403157"]},{"raw_affiliation_string":"Sch. of Autom. & Electr. Eng, Univ. of Sci. & Technol. Beijing, Beijing, China","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021489495","display_name":"Guang\u2010Da Hu","orcid":"https://orcid.org/0000-0002-9590-201X"},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guang-Da Hu","raw_affiliation_strings":["School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China","Sch. of Autom. & Electr. Eng, Univ. of Sci. & Technol. Beijing, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China","institution_ids":["https://openalex.org/I92403157"]},{"raw_affiliation_string":"Sch. of Autom. & Electr. Eng, Univ. of Sci. & Technol. Beijing, Beijing, China","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101512101","display_name":"Yixin Yin","orcid":"https://orcid.org/0000-0001-6056-8878"},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yi-Xin Yin","raw_affiliation_strings":["School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China","Sch. of Autom. & Electr. Eng, Univ. of Sci. & Technol. Beijing, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China","institution_ids":["https://openalex.org/I92403157"]},{"raw_affiliation_string":"Sch. of Autom. & Electr. Eng, Univ. of Sci. & Technol. Beijing, Beijing, China","institution_ids":["https://openalex.org/I92403157"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I92403157"],"apc_list":null,"apc_paid":null,"fwci":2.2457,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.88344887,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"59","issue":"7","first_page":"453","last_page":"457"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9994999766349792,"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":0.9966999888420105,"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/mathematics","display_name":"Mathematics","score":0.7495160698890686},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.7122218012809753},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6591148376464844},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6489685773849487},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5648449659347534},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43480977416038513},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39829331636428833},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07083383202552795},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0700421929359436}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7495160698890686},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7122218012809753},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6591148376464844},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6489685773849487},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5648449659347534},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43480977416038513},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39829331636428833},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07083383202552795},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0700421929359436},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsii.2012.2200172","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsii.2012.2200172","pdf_url":null,"source":{"id":"https://openalex.org/S93916849","display_name":"IEEE Transactions on Circuits & Systems II Express Briefs","issn_l":"1549-7747","issn":["1549-7747","1558-3791"],"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 Circuits and Systems II: Express Briefs","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1482504246","https://openalex.org/W1524186571","https://openalex.org/W1525718855","https://openalex.org/W2004549800","https://openalex.org/W2014316832","https://openalex.org/W2035277082","https://openalex.org/W2036685584","https://openalex.org/W2038137192","https://openalex.org/W2043337752","https://openalex.org/W2047226061","https://openalex.org/W2059331811","https://openalex.org/W2071651841","https://openalex.org/W2090374461","https://openalex.org/W2099885777","https://openalex.org/W2105893362","https://openalex.org/W2111930714","https://openalex.org/W2113589527","https://openalex.org/W2136590653","https://openalex.org/W2147064494","https://openalex.org/W2150663183","https://openalex.org/W2151136609","https://openalex.org/W2155194924","https://openalex.org/W2162053828","https://openalex.org/W2164149907","https://openalex.org/W2166180798","https://openalex.org/W2170125401","https://openalex.org/W4206363472","https://openalex.org/W6676725035"],"related_works":["https://openalex.org/W2154204858","https://openalex.org/W3209622820","https://openalex.org/W2382250648","https://openalex.org/W2367363545","https://openalex.org/W2586383879","https://openalex.org/W2067895158","https://openalex.org/W4379507409","https://openalex.org/W2561874146","https://openalex.org/W2066331732","https://openalex.org/W2077468606"],"abstract_inverted_index":{"This":[0],"brief":[1],"is":[2,35,46],"concerned":[3],"with":[4],"the":[5,30],"Lyapunov-type":[6,62],"stability":[7,31],"theorem":[8],"of":[9],"general":[10,39],"2-D":[11,40],"nonlinear":[12,41],"parameter-varying":[13,42],"Fornasini-Marchesini":[14],"(FM)":[15],"second":[16,44],"model.":[17],"First,":[18],"three":[19],"comparison":[20],"lemmas":[21],"are":[22],"given":[23],"and":[24,53],"play":[25],"an":[26],"important":[27],"role":[28],"in":[29],"analysis.":[32],"Then,":[33],"it":[34,57],"shown":[36],"that":[37],"a":[38,59],"FM":[43],"model":[45],"uniformly":[47,50],"stable":[48,52],"(or":[49],"asymptotically":[51],"exponentially":[54],"stable)":[55],"if":[56],"admits":[58],"corresponding":[60],"continuous":[61],"function.":[63]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}