{"id":"https://openalex.org/W2069354092","doi":"https://doi.org/10.1109/tac.2012.2209260","title":"A Strict Control Lyapunov Function for a Diffusion Equation With Time-Varying Distributed Coefficients","display_name":"A Strict Control Lyapunov Function for a Diffusion Equation With Time-Varying Distributed Coefficients","publication_year":2012,"publication_date":"2012-07-19","ids":{"openalex":"https://openalex.org/W2069354092","doi":"https://doi.org/10.1109/tac.2012.2209260","mag":"2069354092"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2012.2209260","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2012.2209260","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00719502","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111517295","display_name":"Federico Bribiesca Argomedo","orcid":"https://orcid.org/0000-0002-2389-4241"},"institutions":[{"id":"https://openalex.org/I106785703","display_name":"Institut polytechnique de Grenoble","ror":"https://ror.org/05sbt2524","country_code":"FR","type":"education","lineage":["https://openalex.org/I106785703","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]},{"id":"https://openalex.org/I4210124956","display_name":"GIPSA-Lab","ror":"https://ror.org/02wrme198","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR","US"],"is_corresponding":false,"raw_author_name":"Federico Bribiesca Argomedo","raw_affiliation_strings":["CNRS, GIPSA-Laboratory UMR 5216, Universit\u00e9 de Grenoble, Grenoble, France","Department of Mechanical and AeroSpace Engineering, University of California, San Diego, La Jolla, CA, USA","GIPSA - Syst\u00e8mes lin\u00e9aires et robustesse","GIPSA - Syst\u00e8mes non lin\u00e9aires et complexit\u00e9"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS, GIPSA-Laboratory UMR 5216, Universit\u00e9 de Grenoble, Grenoble, France","institution_ids":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006"]},{"raw_affiliation_string":"Department of Mechanical and AeroSpace Engineering, University of California, San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"GIPSA - Syst\u00e8mes lin\u00e9aires et robustesse","institution_ids":["https://openalex.org/I4210124956"]},{"raw_affiliation_string":"GIPSA - Syst\u00e8mes non lin\u00e9aires et complexit\u00e9","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083387069","display_name":"Christophe Prieur","orcid":"https://orcid.org/0000-0002-4456-2019"},"institutions":[{"id":"https://openalex.org/I106785703","display_name":"Institut polytechnique de Grenoble","ror":"https://ror.org/05sbt2524","country_code":"FR","type":"education","lineage":["https://openalex.org/I106785703","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210124956","display_name":"GIPSA-Lab","ror":"https://ror.org/02wrme198","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Christophe Prieur","raw_affiliation_strings":["CNRS, GIPSA-Laboratory UMR 5216, Universit\u00e9 de Grenoble, Grenoble, France","GIPSA - Syst\u00e8mes non lin\u00e9aires et complexit\u00e9"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS, GIPSA-Laboratory UMR 5216, Universit\u00e9 de Grenoble, Grenoble, France","institution_ids":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006"]},{"raw_affiliation_string":"GIPSA - Syst\u00e8mes non lin\u00e9aires et complexit\u00e9","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029011489","display_name":"Emmanuel Witrant","orcid":"https://orcid.org/0000-0002-2026-8915"},"institutions":[{"id":"https://openalex.org/I106785703","display_name":"Institut polytechnique de Grenoble","ror":"https://ror.org/05sbt2524","country_code":"FR","type":"education","lineage":["https://openalex.org/I106785703","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210124956","display_name":"GIPSA-Lab","ror":"https://ror.org/02wrme198","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Emmanuel Witrant","raw_affiliation_strings":["CNRS, GIPSA-Laboratory UMR 5216, Universit\u00e9 de Grenoble, Grenoble, France","GIPSA - Syst\u00e8mes lin\u00e9aires et robustesse"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS, GIPSA-Laboratory UMR 5216, Universit\u00e9 de Grenoble, Grenoble, France","institution_ids":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006"]},{"raw_affiliation_string":"GIPSA - Syst\u00e8mes lin\u00e9aires et robustesse","institution_ids":["https://openalex.org/I4210124956"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031325484","display_name":"S. Br\u00e9mond","orcid":null},"institutions":[{"id":"https://openalex.org/I2738703131","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131"]},{"id":"https://openalex.org/I4210110641","display_name":"CEA Cadarache","ror":"https://ror.org/01rs1gy10","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131","https://openalex.org/I4210110641"]},{"id":"https://openalex.org/I4210142114","display_name":"Institut de Recherche sur la Fusion par confinement Magn\u00e9tique","ror":"https://ror.org/03hffat62","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131","https://openalex.org/I2738703131","https://openalex.org/I4210113668","https://openalex.org/I4210142114"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Sylvain Bremond","raw_affiliation_strings":["CEA, Saint-Paul-lez-Durance, France","Institut de Recherche sur la Fusion par confinement Magn\u00e9tique"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CEA, Saint-Paul-lez-Durance, France","institution_ids":["https://openalex.org/I2738703131","https://openalex.org/I4210110641"]},{"raw_affiliation_string":"Institut de Recherche sur la Fusion par confinement Magn\u00e9tique","institution_ids":["https://openalex.org/I4210142114"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":8,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":18.0768,"has_fulltext":false,"cited_by_count":105,"citation_normalized_percentile":{"value":0.99085196,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":100},"biblio":{"volume":"58","issue":"2","first_page":"290","last_page":"303"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","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/T11110","display_name":"Stability and Controllability of Differential Equations","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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.7897053956985474},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.7455762624740601},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6976030468940735},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.45878058671951294},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.44418755173683167},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.4315766990184784},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41924363374710083},{"id":"https://openalex.org/keywords/lyapunov-stability","display_name":"Lyapunov stability","score":0.4115103781223297},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40211260318756104},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1095905601978302},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08604657649993896}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7897053956985474},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7455762624740601},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6976030468940735},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.45878058671951294},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.44418755173683167},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.4315766990184784},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41924363374710083},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.4115103781223297},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40211260318756104},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1095905601978302},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08604657649993896},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2012.2209260","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2012.2209260","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00719502v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00719502","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, 2013, 58 (2), pp.290-303. &#x27E8;10.1109/TAC.2012.2209260&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00719502v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00719502","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, 2013, 58 (2), pp.290-303. &#x27E8;10.1109/TAC.2012.2209260&#x27E9;","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"score":0.8199999928474426,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W563110697","https://openalex.org/W1496662771","https://openalex.org/W1502019808","https://openalex.org/W1971911319","https://openalex.org/W1974777461","https://openalex.org/W1990575755","https://openalex.org/W1998919214","https://openalex.org/W2002489263","https://openalex.org/W2004132268","https://openalex.org/W2006061153","https://openalex.org/W2019689017","https://openalex.org/W2028161232","https://openalex.org/W2033549247","https://openalex.org/W2036896457","https://openalex.org/W2051835655","https://openalex.org/W2063708295","https://openalex.org/W2065060801","https://openalex.org/W2065109483","https://openalex.org/W2073696585","https://openalex.org/W2078854980","https://openalex.org/W2095133429","https://openalex.org/W2111955474","https://openalex.org/W2114094279","https://openalex.org/W2119967247","https://openalex.org/W2120748789","https://openalex.org/W2121440005","https://openalex.org/W2126159667","https://openalex.org/W2126235488","https://openalex.org/W2132871031","https://openalex.org/W2134733687","https://openalex.org/W2138693236","https://openalex.org/W2149882063","https://openalex.org/W2160550968","https://openalex.org/W2167587160","https://openalex.org/W2568793017","https://openalex.org/W4298576603","https://openalex.org/W4302061159","https://openalex.org/W6648200028","https://openalex.org/W6663418328","https://openalex.org/W6666670556"],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W2383986032","https://openalex.org/W3194517843","https://openalex.org/W2374426356","https://openalex.org/W2121515234","https://openalex.org/W2059628530","https://openalex.org/W2164487476","https://openalex.org/W1977987201","https://openalex.org/W2210722882","https://openalex.org/W2534107666"],"abstract_inverted_index":{"In":[0],"this":[1,39],"paper,":[2],"a":[3,22,42,99,113,166,186],"strict":[4],"Lyapunov":[5,40],"function":[6],"is":[7,45,73,94,149],"developed":[8],"in":[9,69,96,106,145,179],"order":[10],"to":[11,47,64,120,151,157,201],"show":[12,194],"the":[13,49,53,70,76,80,83,86,103,121,127,134,146,158,163,170,180],"exponential":[14],"stability":[15,18],"and":[16,55,66,90,132,183,197],"input-to-state":[17],"(ISS)":[19],"properties":[20,51],"of":[21,52,82,88,98,102,116,165,188],"diffusion":[23,109],"equation":[24],"for":[25,126],"nonhomogeneous":[26],"media.":[27],"Such":[28],"media":[29],"can":[30],"involve":[31,112],"rapidly":[32],"time-varying":[33],"distributed":[34,71],"diffusivity":[35],"coefficients.":[36],"Based":[37],"on":[38,75,85],"function,":[41],"control":[43,104,125,139,172],"law":[44,140],"derived":[46],"preserve":[48],"ISS":[50,91],"system":[54],"improve":[56],"its":[57],"performance.":[58],"A":[59,137],"robustness":[60,198],"analysis":[61],"with":[62,162,199],"respect":[63,200],"disturbances":[65],"estimation":[67],"errors":[68],"parameters":[72],"performed":[74],"system,":[77],"precisely":[78],"showing":[79],"impact":[81],"controller":[84],"rate":[87],"convergence":[89],"gains.":[92],"This":[93],"important":[95],"light":[97],"possible":[100,156],"implementation":[101],"since,":[105],"most":[107],"cases,":[108],"coefficient":[110],"estimates":[111],"high":[114],"degree":[115],"uncertainty.":[117],"An":[118],"application":[119],"safety":[122],"factor":[123],"profile":[124],"Tore":[128,189],"Supra":[129,190],"tokamak":[130],"illustrates":[131],"motivates":[133],"theoretical":[135],"results.":[136],"constrained":[138],"(incorporating":[141],"nonlinear":[142],"shape":[143],"constraints":[144],"actuation":[147],"profiles)":[148],"designed":[150],"behave":[152],"as":[153,155],"close":[154],"unconstrained":[159],"version,":[160],"albeit":[161],"equivalent":[164],"variable":[167],"gain.":[168],"Finally,":[169],"proposed":[171],"laws":[173],"are":[174],"tested":[175],"under":[176],"simulation,":[177],"first":[178],"nominal":[181],"case":[182],"then":[184],"using":[185],"model":[187],"dynamics,":[191],"where":[192],"they":[193],"adequate":[195],"performance":[196],"disturbances.":[202]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2016-06-24T00:00:00"}
