{"id":"https://openalex.org/W2570988044","doi":"https://doi.org/10.1109/cdc.2016.7799138","title":"Multivariable PI controller design for 2 \u00d7 2 systems governed by hyperbolic partial differential equations with Lyapunov techniques","display_name":"Multivariable PI controller design for 2 \u00d7 2 systems governed by hyperbolic partial differential equations with Lyapunov techniques","publication_year":2016,"publication_date":"2016-12-01","ids":{"openalex":"https://openalex.org/W2570988044","doi":"https://doi.org/10.1109/cdc.2016.7799138","mag":"2570988044"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2016.7799138","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2016.7799138","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE 55th Conference on Decision and Control (CDC)","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/A5005278194","display_name":"Ngoc-Tu Trinh","orcid":null},"institutions":[{"id":"https://openalex.org/I4210143168","display_name":"Laboratoire d'Automatique, de G\u00e9nie des Proc\u00e9d\u00e9s et de G\u00e9nie Pharmaceutique","ror":"https://ror.org/03kfjwy31","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210095849","https://openalex.org/I4210143168","https://openalex.org/I59692284"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ngoc-Tu Trinh","raw_affiliation_strings":["B\u00e2timent CPE, Laboratory LAGEP, Villeurbanne Cedex, France","Laboratoire d'automatique et de g\u00e9nie des proc\u00e9d\u00e9s"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"B\u00e2timent CPE, Laboratory LAGEP, Villeurbanne Cedex, France","institution_ids":["https://openalex.org/I4210143168"]},{"raw_affiliation_string":"Laboratoire d'automatique et de g\u00e9nie des proc\u00e9d\u00e9s","institution_ids":["https://openalex.org/I4210143168"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082790000","display_name":"Vincent Andrieu","orcid":"https://orcid.org/0000-0003-1877-6205"},"institutions":[{"id":"https://openalex.org/I4210143168","display_name":"Laboratoire d'Automatique, de G\u00e9nie des Proc\u00e9d\u00e9s et de G\u00e9nie Pharmaceutique","ror":"https://ror.org/03kfjwy31","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210095849","https://openalex.org/I4210143168","https://openalex.org/I59692284"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Vincent Andrieu","raw_affiliation_strings":["B\u00e2timent CPE, Laboratory LAGEP, Villeurbanne Cedex, France","Laboratoire d'automatique et de g\u00e9nie des proc\u00e9d\u00e9s"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"B\u00e2timent CPE, Laboratory LAGEP, Villeurbanne Cedex, France","institution_ids":["https://openalex.org/I4210143168"]},{"raw_affiliation_string":"Laboratoire d'automatique et de g\u00e9nie des proc\u00e9d\u00e9s","institution_ids":["https://openalex.org/I4210143168"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004417909","display_name":"Cheng-Zhong Xu","orcid":"https://orcid.org/0000-0003-1622-778X"},"institutions":[{"id":"https://openalex.org/I4210143168","display_name":"Laboratoire d'Automatique, de G\u00e9nie des Proc\u00e9d\u00e9s et de G\u00e9nie Pharmaceutique","ror":"https://ror.org/03kfjwy31","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210095849","https://openalex.org/I4210143168","https://openalex.org/I59692284"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cheng-Zhong Xu","raw_affiliation_strings":["B\u00e2timent CPE, Laboratory LAGEP, Villeurbanne Cedex, France","Laboratoire d'automatique et de g\u00e9nie des proc\u00e9d\u00e9s"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"B\u00e2timent CPE, Laboratory LAGEP, Villeurbanne Cedex, France","institution_ids":["https://openalex.org/I4210143168"]},{"raw_affiliation_string":"Laboratoire d'automatique et de g\u00e9nie des proc\u00e9d\u00e9s","institution_ids":["https://openalex.org/I4210143168"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210143168"],"apc_list":null,"apc_paid":null,"fwci":1.7615,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.83886185,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"5654","last_page":"5659"},"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":0.9998000264167786,"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/T11110","display_name":"Stability and Controllability of Differential Equations","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/T11416","display_name":"Numerical methods for differential equations","score":0.988099992275238,"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"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9743000268936157,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"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":0.6901372671127319},{"id":"https://openalex.org/keywords/multivariable-calculus","display_name":"Multivariable calculus","score":0.6804889440536499},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6213068962097168},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5887852311134338},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5676271915435791},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5340149998664856},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.52695232629776},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4782063961029053},{"id":"https://openalex.org/keywords/geometric-function-theory","display_name":"Geometric function theory","score":0.41547706723213196},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37174004316329956},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3228521943092346},{"id":"https://openalex.org/keywords/riemann-surface","display_name":"Riemann surface","score":0.2938772439956665},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26054710149765015},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.14859545230865479},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.13420721888542175},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11640390753746033},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.10874944925308228}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6901372671127319},{"id":"https://openalex.org/C117312493","wikidata":"https://www.wikidata.org/wiki/Q2035437","display_name":"Multivariable calculus","level":2,"score":0.6804889440536499},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6213068962097168},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5887852311134338},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5676271915435791},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5340149998664856},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.52695232629776},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4782063961029053},{"id":"https://openalex.org/C112468886","wikidata":"https://www.wikidata.org/wiki/Q5535485","display_name":"Geometric function theory","level":3,"score":0.41547706723213196},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37174004316329956},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3228521943092346},{"id":"https://openalex.org/C18556879","wikidata":"https://www.wikidata.org/wiki/Q753035","display_name":"Riemann surface","level":2,"score":0.2938772439956665},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26054710149765015},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.14859545230865479},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.13420721888542175},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11640390753746033},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.10874944925308228},{"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/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","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/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2016.7799138","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2016.7799138","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE 55th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-01923332v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01923332","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the 2016 IEEE 55th Conference on Decision and Control (CDC), 2016, Las Vegas, USA, Unknown Region. pp.5654-5659, &#x27E8;10.1109/CDC.2016.7799138&#x27E9;","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1534230689","https://openalex.org/W1591390169","https://openalex.org/W1974777461","https://openalex.org/W2002489263","https://openalex.org/W2016630129","https://openalex.org/W2086906338","https://openalex.org/W2095201412","https://openalex.org/W2118360955","https://openalex.org/W2120281474","https://openalex.org/W2133904990","https://openalex.org/W2134282505","https://openalex.org/W2151460005","https://openalex.org/W2155059872","https://openalex.org/W2162853993","https://openalex.org/W2333711310","https://openalex.org/W2961546808","https://openalex.org/W4298576603","https://openalex.org/W6631988634","https://openalex.org/W6765506672"],"related_works":["https://openalex.org/W1576377477","https://openalex.org/W2721687755","https://openalex.org/W2224575301","https://openalex.org/W418212511","https://openalex.org/W2388146630","https://openalex.org/W2086932047","https://openalex.org/W2099048101","https://openalex.org/W1964208669","https://openalex.org/W4300349471","https://openalex.org/W2800947864"],"abstract_inverted_index":{"This":[0],"paper":[1],"addresses":[2],"the":[3,21,25,31,34,39,46,53,69,75,91,94],"multivariable":[4],"PI":[5,47,77,96],"regulation":[6,67],"control":[7,23],"of":[8,11,42,68,93],"a":[9,58,80],"class":[10],"linear":[12],"systems":[13],"described":[14],"by":[15],"hyperbolic":[16],"partial":[17],"differential":[18],"equations.":[19],"Both":[20],"input":[22],"and":[24,45,66,84],"output":[26],"measurement":[27],"are":[28],"situated":[29],"on":[30],"boundary.":[32],"First,":[33],"system":[35],"is":[36,50,61],"transformed":[37],"into":[38],"characteristic":[40],"form":[41],"Riemann":[43,54],"invariants,":[44],"controller":[48,78],"design":[49],"proposed":[51],"for":[52,79],"invariant":[55],"system.":[56,71],"Then,":[57],"Lyapunov":[59],"functional":[60],"constructed":[62],"to":[63,89],"prove":[64],"stabilization":[65],"closed-loop":[70],"Finally,":[72],"we":[73],"apply":[74],"designed":[76,95],"nonlinear":[81],"Saint-Venant":[82],"model":[83],"carry":[85],"out":[86],"numerical":[87],"simulations":[88],"evaluate":[90],"performances":[92],"controller.":[97]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2017-01-13T00:00:00"}
