{"id":"https://openalex.org/W1999318857","doi":"https://doi.org/10.1109/acc.2012.6314688","title":"Collocated output-feedback stabilization of a 2 &amp;#x00D7; 2 quasilinear hyperbolic system using backstepping","display_name":"Collocated output-feedback stabilization of a 2 &amp;#x00D7; 2 quasilinear hyperbolic system using backstepping","publication_year":2012,"publication_date":"2012-06-01","ids":{"openalex":"https://openalex.org/W1999318857","doi":"https://doi.org/10.1109/acc.2012.6314688","mag":"1999318857"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2012.6314688","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2012.6314688","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 American Control Conference (ACC)","raw_type":"proceedings-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/A5071603624","display_name":"Rafael V\u00e1zquez","orcid":"https://orcid.org/0000-0001-6904-2055"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"R. Vazquez","raw_affiliation_strings":["Department of AeroSpace Engineering, Universidad de Sevilla, Seville, Spain"],"affiliations":[{"raw_affiliation_string":"Department of AeroSpace Engineering, Universidad de Sevilla, Seville, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083872718","display_name":"Jean\u2010Michel Coron","orcid":"https://orcid.org/0000-0002-2457-8873"},"institutions":[{"id":"https://openalex.org/I185839726","display_name":"Institut Universitaire de France","ror":"https://ror.org/055khg266","country_code":"FR","type":"education","lineage":["https://openalex.org/I185839726"]},{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"J. Coron","raw_affiliation_strings":["Institut Universitaire de France, Paris, France","Laboratoire Jacques-Louis Lions, University Pierre et Marie Curie, France"],"affiliations":[{"raw_affiliation_string":"Institut Universitaire de France, Paris, France","institution_ids":["https://openalex.org/I185839726"]},{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions, University Pierre et Marie Curie, France","institution_ids":["https://openalex.org/I4210158291"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018293076","display_name":"Miroslav Krsti\u0107","orcid":"https://orcid.org/0000-0002-5523-941X"},"institutions":[{"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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Krstic","raw_affiliation_strings":["Department of Mechanical and AeroSpace Engineering, University of California, San Diego, La Jolla, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and AeroSpace Engineering, University of California, San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046711023","display_name":"Georges Bastin","orcid":"https://orcid.org/0000-0003-1447-2466"},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"G. Bastin","raw_affiliation_strings":["Department of Mathematical Engineering, Universite Catholique de Louvain, Louvain-la-Neuve, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Engineering, Universite Catholique de Louvain, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5071603624"],"corresponding_institution_ids":["https://openalex.org/I79238269"],"apc_list":null,"apc_paid":null,"fwci":6.1934,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.95975153,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"2202","last_page":"2207"},"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":0.9787999987602234,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9384999871253967,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/backstepping","display_name":"Backstepping","score":0.9640288949012756},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.7206887602806091},{"id":"https://openalex.org/keywords/observer","display_name":"Observer (physics)","score":0.6228306293487549},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5700543522834778},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5559727549552917},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5486300587654114},{"id":"https://openalex.org/keywords/hyperbolic-partial-differential-equation","display_name":"Hyperbolic partial differential equation","score":0.5115824341773987},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.4948996901512146},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46818768978118896},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.46718671917915344},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4555150866508484},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4424494504928589},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.431255042552948},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35354524850845337},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32787424325942993},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31481799483299255},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.2843858003616333},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.23523050546646118},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.2084662914276123},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.17497411370277405},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1370997428894043},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12167897820472717},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0589471161365509}],"concepts":[{"id":"https://openalex.org/C72218879","wikidata":"https://www.wikidata.org/wiki/Q4839759","display_name":"Backstepping","level":4,"score":0.9640288949012756},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7206887602806091},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.6228306293487549},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5700543522834778},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5559727549552917},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5486300587654114},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.5115824341773987},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.4948996901512146},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46818768978118896},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.46718671917915344},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4555150866508484},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4424494504928589},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.431255042552948},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35354524850845337},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32787424325942993},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31481799483299255},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2843858003616333},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.23523050546646118},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.2084662914276123},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.17497411370277405},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1370997428894043},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12167897820472717},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0589471161365509},{"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2012.6314688","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2012.6314688","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 American Control Conference (ACC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.7900000214576721,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W564609686","https://openalex.org/W585700782","https://openalex.org/W1550066393","https://openalex.org/W1972974005","https://openalex.org/W1973025870","https://openalex.org/W1974777461","https://openalex.org/W2002489263","https://openalex.org/W2016630129","https://openalex.org/W2036900764","https://openalex.org/W2084586390","https://openalex.org/W2108789625","https://openalex.org/W2110837625","https://openalex.org/W2111189221","https://openalex.org/W2127231563","https://openalex.org/W2132545516","https://openalex.org/W2136938755","https://openalex.org/W2139048369","https://openalex.org/W2161311867","https://openalex.org/W2162853993","https://openalex.org/W2172542352","https://openalex.org/W2178205091","https://openalex.org/W2499641798","https://openalex.org/W3144501209","https://openalex.org/W4298576603","https://openalex.org/W6676443084","https://openalex.org/W6680425146"],"related_works":["https://openalex.org/W2771027241","https://openalex.org/W1765905465","https://openalex.org/W2164703465","https://openalex.org/W2168383058","https://openalex.org/W2143247663","https://openalex.org/W2050693590","https://openalex.org/W2939409110","https://openalex.org/W1974207849","https://openalex.org/W2382994547","https://openalex.org/W2528099681"],"abstract_inverted_index":{"We":[0,22],"consider":[1],"the":[2,38,50,60,69,82,97],"problem":[3],"of":[4,13,37,49,55,62,90],"output":[5,25,76],"feedback":[6,26,73],"stabilization":[7],"for":[8,85],"a":[9,63,100],"quasilinear":[10],"2\u00d72":[11],"system":[12,89],"first-order":[14,91],"hyperbolic":[15,92],"PDEs":[16],"with":[17,29],"boundary":[18],"actuation":[19,30],"and":[20,31,40,75],"measurement.":[21],"design":[23],"an":[24],"control":[27],"law,":[28],"measurement":[32],"on":[33,59],"only":[34],"one":[35],"end":[36],"domain,":[39],"prove":[41],"local":[42],"H":[43],"<sup":[44],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[45],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[46],"exponential":[47],"stability":[48,56],"closed-loop":[51],"system.":[52],"The":[53,72],"proof":[54],"is":[57,104],"based":[58],"construction":[61],"strict":[64],"Lyapunov":[65],"function":[66],"which":[67,103],"includes":[68],"observer":[70],"states.":[71],"law":[74],"injection":[77],"gains":[78],"are":[79],"found":[80],"using":[81],"backstepping":[83],"method":[84],"2":[86,88],"\u00d7":[87],"linear":[93],"PDEs,":[94],"developed":[95],"by":[96],"authors":[98],"in":[99],"previous":[101],"work,":[102],"briefly":[105],"reviewed.":[106]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
