{"id":"https://openalex.org/W2039230101","doi":"https://doi.org/10.1080/00207170701338867","title":"Exponential stability and stabilization of uncertain linear time-varying systems using parameter dependent Lyapunov function","display_name":"Exponential stability and stabilization of uncertain linear time-varying systems using parameter dependent Lyapunov function","publication_year":2007,"publication_date":"2007-08-01","ids":{"openalex":"https://openalex.org/W2039230101","doi":"https://doi.org/10.1080/00207170701338867","mag":"2039230101"},"language":"en","primary_location":{"id":"doi:10.1080/00207170701338867","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170701338867","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","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/A5064061692","display_name":"Vu N. Phat","orcid":"https://orcid.org/0000-0001-9467-6674"},"institutions":[{"id":"https://openalex.org/I4210148301","display_name":"Institute of Mathematics","ror":"https://ror.org/04jr71r83","country_code":"VN","type":"facility","lineage":["https://openalex.org/I4210148301","https://openalex.org/I70349855"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"V. N. Phat","raw_affiliation_strings":["Institute of Mathematics , 18 Hoang Quoc Viet Road, Hanoi, Vietnam"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics , 18 Hoang Quoc Viet Road, Hanoi, Vietnam","institution_ids":["https://openalex.org/I4210148301"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077573795","display_name":"Phan Th\u00e0nh Nam","orcid":"https://orcid.org/0000-0002-3730-8864"},"institutions":[{"id":"https://openalex.org/I4210137358","display_name":"Quy Nhon University","ror":"https://ror.org/04h4y6q56","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210137358"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"P. T. Nam","raw_affiliation_strings":["Department of Mathematics , Quinhon University , Quinhon City, Vietnam"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Quinhon University , Quinhon City, Vietnam","institution_ids":["https://openalex.org/I4210137358"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064061692"],"corresponding_institution_ids":["https://openalex.org/I4210148301"],"apc_list":null,"apc_paid":null,"fwci":7.8383,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.96985773,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"80","issue":"8","first_page":"1333","last_page":"1341"},"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9918000102043152,"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/T11236","display_name":"Control Systems and Identification","score":0.987500011920929,"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":0.7306426763534546},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6925781965255737},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6120198369026184},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5337650775909424},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5245487689971924},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.4942910671234131},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4704799950122833},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.43538686633110046},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.431172251701355},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.42984092235565186},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4106595814228058},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4101184606552124},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3178122043609619},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2485240399837494},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1539139449596405},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13647615909576416},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.07277840375900269}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7306426763534546},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6925781965255737},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6120198369026184},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5337650775909424},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5245487689971924},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.4942910671234131},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4704799950122833},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.43538686633110046},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.431172251701355},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.42984092235565186},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4106595814228058},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4101184606552124},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3178122043609619},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2485240399837494},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1539139449596405},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13647615909576416},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.07277840375900269},{"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},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207170701338867","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170701338867","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7599999904632568,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W582868771","https://openalex.org/W1967624116","https://openalex.org/W1975170630","https://openalex.org/W1978271437","https://openalex.org/W1996558596","https://openalex.org/W2009893907","https://openalex.org/W2022706157","https://openalex.org/W2022884092","https://openalex.org/W2024720874","https://openalex.org/W2030387966","https://openalex.org/W2035547598","https://openalex.org/W2039015886","https://openalex.org/W2044464896","https://openalex.org/W2073514351","https://openalex.org/W2075933120","https://openalex.org/W2083857189","https://openalex.org/W2104543311","https://openalex.org/W2120452688","https://openalex.org/W2122184472","https://openalex.org/W2128767191","https://openalex.org/W2143142281","https://openalex.org/W2148926497","https://openalex.org/W2151464749","https://openalex.org/W2152098405","https://openalex.org/W2154866585","https://openalex.org/W3210839039","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W2383986032","https://openalex.org/W2534107666","https://openalex.org/W3194517843","https://openalex.org/W2121515234","https://openalex.org/W1977987201","https://openalex.org/W2059628530","https://openalex.org/W2210722882","https://openalex.org/W1025006035","https://openalex.org/W2164487476"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,28,52,75],"problem":[4],"of":[5,13,44,81],"exponential":[6,53],"stability":[7,46,54],"and":[8,27,55,92],"stabilization":[9,56],"for":[10,51],"a":[11,25,41,64],"class":[12],"uncertain":[14],"linear":[15,83],"time-varying":[16,29,42],"systems":[17],"is":[18],"considered.":[19],"The":[20,97],"system":[21],"matrix":[22,84],"belongs":[23],"to":[24],"polytope":[26],"parameter":[30,58,71],"as":[31,33],"well":[32],"its":[34],"time":[35],"derivative":[36],"are":[37,68,77,94,99],"bounded.":[38],"Based":[39],"on":[40],"version":[43],"Lyapunov":[45,73],"theorem,":[47],"new":[48],"sufficient":[49],"conditions":[50,76],"via":[57],"dependent":[59,72],"state":[60],"feedback":[61],"controllers":[62],"(i.e.,":[63],"gain":[65],"scheduling":[66],"controllers)":[67],"given.":[69],"Using":[70],"function,":[74],"formulated":[78],"in":[79],"terms":[80],"two":[82],"inequalities":[85],"without":[86],"introducing":[87],"extra":[88],"useless":[89],"decision":[90],"variables":[91],"hence":[93],"simply":[95],"verified.":[96],"results":[98],"illustrated":[100],"by":[101],"numerical":[102],"examples.":[103]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}