{"id":"https://openalex.org/W1516577293","doi":"https://doi.org/10.2478/v10006-012-0041-6","title":"A multi-model approach to Saint-Venant equations: A stability study by LMIs","display_name":"A multi-model approach to Saint-Venant equations: A stability study by LMIs","publication_year":2012,"publication_date":"2012-09-01","ids":{"openalex":"https://openalex.org/W1516577293","doi":"https://doi.org/10.2478/v10006-012-0041-6","mag":"1516577293"},"language":"en","primary_location":{"id":"doi:10.2478/v10006-012-0041-6","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-012-0041-6","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-012-0041-6","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://sciendo.com/pdf/10.2478/v10006-012-0041-6","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054975000","display_name":"Val\u00e9rie Dos Santos Martins","orcid":"https://orcid.org/0000-0003-1578-4736"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210143168","display_name":"Automation and Process Engineering Laboratory","ror":"https://ror.org/03kfjwy31","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210095849","https://openalex.org/I4210143168","https://openalex.org/I59692284"]},{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Val\u00e9rie Dos Santos Martins","raw_affiliation_strings":["Automatic and Process Control Laboratory (LAGEP) University of Lyon 1, CNRS, UMR 5007, Villeurbanne F-69622, France","Automatic and Process Control Laboratory (LAGEP), University of Lyon 1, CNRS, UMR 5007, Villeurbanne F-69622, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Automatic and Process Control Laboratory (LAGEP) University of Lyon 1, CNRS, UMR 5007, Villeurbanne F-69622, France","institution_ids":["https://openalex.org/I4210143168","https://openalex.org/I100532134","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Automatic and Process Control Laboratory (LAGEP), University of Lyon 1, CNRS, UMR 5007, Villeurbanne F-69622, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028895640","display_name":"Micka\u00ebl Rodrigues","orcid":"https://orcid.org/0000-0003-3201-0943"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210143168","display_name":"Automation and Process Engineering Laboratory","ror":"https://ror.org/03kfjwy31","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210095849","https://openalex.org/I4210143168","https://openalex.org/I59692284"]},{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mickael Rodrigues","raw_affiliation_strings":["Automatic and Process Control Laboratory (LAGEP) University of Lyon 1, CNRS, UMR 5007, Villeurbanne F-69622, France","Automatic and Process Control Laboratory (LAGEP), University of Lyon 1, CNRS, UMR 5007, Villeurbanne F-69622, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Automatic and Process Control Laboratory (LAGEP) University of Lyon 1, CNRS, UMR 5007, Villeurbanne F-69622, France","institution_ids":["https://openalex.org/I4210143168","https://openalex.org/I100532134","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Automatic and Process Control Laboratory (LAGEP), University of Lyon 1, CNRS, UMR 5007, Villeurbanne F-69622, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057892393","display_name":"Mamadou Diagne","orcid":"https://orcid.org/0000-0001-5597-7669"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I4210143168","display_name":"Automation and Process Engineering Laboratory","ror":"https://ror.org/03kfjwy31","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210095849","https://openalex.org/I4210143168","https://openalex.org/I59692284"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mamadou Diagne","raw_affiliation_strings":["Automatic and Process Control Laboratory (LAGEP) University of Lyon 1, CNRS, UMR 5007, Villeurbanne F-69622, France","Automatic and Process Control Laboratory (LAGEP), University of Lyon 1, CNRS, UMR 5007, Villeurbanne F-69622, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Automatic and Process Control Laboratory (LAGEP) University of Lyon 1, CNRS, UMR 5007, Villeurbanne F-69622, France","institution_ids":["https://openalex.org/I4210143168","https://openalex.org/I100532134","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Automatic and Process Control Laboratory (LAGEP), University of Lyon 1, CNRS, UMR 5007, Villeurbanne F-69622, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5054975000"],"corresponding_institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I4210143168"],"apc_list":{"value":4080,"currency":"PLN","value_usd":1100},"apc_paid":{"value":4080,"currency":"PLN","value_usd":1100},"fwci":2.8413,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.90367699,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"22","issue":"3","first_page":"539","last_page":"550"},"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":0.9986000061035156,"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":0.9986000061035156,"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":0.9977999925613403,"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/T12772","display_name":"Control and Stability of Dynamical 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/nonlinear-system","display_name":"Nonlinear system","score":0.7030187249183655},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5611316561698914},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5527339577674866},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5046933889389038},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5004227161407471},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49094465374946594},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4865492880344391},{"id":"https://openalex.org/keywords/lti-system-theory","display_name":"LTI system theory","score":0.48610973358154297},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4806341230869293},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3166327476501465},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31469374895095825},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.2688203454017639},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.15161392092704773},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10165372490882874}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7030187249183655},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5611316561698914},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5527339577674866},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5046933889389038},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5004227161407471},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49094465374946594},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4865492880344391},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.48610973358154297},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4806341230869293},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3166327476501465},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31469374895095825},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2688203454017639},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.15161392092704773},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10165372490882874},{"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/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","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},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.2478/v10006-012-0041-6","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-012-0041-6","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-012-0041-6","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.1000.1680","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1000.1680","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.baztech-article-BPZ7-0007-0004/c/httpswww_amcs_uz_zgora_plactiondownloadpdfamcs20122234.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00701005v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00701005","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":"International Journal of Applied Mathematics and Computer Science, 2012, 22 (3), pp.539-550. &#x27E8;10.2478/v10006-012-0041-6&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:27d0efaec3a64effa8da501c95121ad5","is_oa":true,"landing_page_url":"https://doaj.org/article/27d0efaec3a64effa8da501c95121ad5","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Applied Mathematics and Computer Science, Vol 22, Iss 3, Pp 539-550 (2012)","raw_type":"article"},{"id":"pmh:oai:zbc.uz.zgora.pl:47008","is_oa":false,"landing_page_url":"https://zbc.uz.zgora.pl/dlibra/docmetadata?showContent=true&id=47008","pdf_url":null,"source":{"id":"https://openalex.org/S4306400400","display_name":"Digital library of Zielona Gora (University of Zielona G\u00f3ra)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I46305939","host_organization_name":"University of Zielona G\u00f3ra","host_organization_lineage":["https://openalex.org/I46305939"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.amcs.uz.zgora.pl/?action=paper&paper=632","raw_type":"artyku\u0142"}],"best_oa_location":{"id":"doi:10.2478/v10006-012-0041-6","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-012-0041-6","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-012-0041-6","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1516577293.pdf","grobid_xml":"https://content.openalex.org/works/W1516577293.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W6120008","https://openalex.org/W14536190","https://openalex.org/W162138997","https://openalex.org/W1508592550","https://openalex.org/W1516829775","https://openalex.org/W1530730921","https://openalex.org/W1538686203","https://openalex.org/W1545557420","https://openalex.org/W1550066393","https://openalex.org/W1600234331","https://openalex.org/W1974543079","https://openalex.org/W1974777461","https://openalex.org/W1997940488","https://openalex.org/W2016630129","https://openalex.org/W2017068231","https://openalex.org/W2025990627","https://openalex.org/W2027300760","https://openalex.org/W2027501711","https://openalex.org/W2035121115","https://openalex.org/W2042227499","https://openalex.org/W2042849642","https://openalex.org/W2042869767","https://openalex.org/W2044402949","https://openalex.org/W2069913713","https://openalex.org/W2071859256","https://openalex.org/W2081044987","https://openalex.org/W2101521115","https://openalex.org/W2102889792","https://openalex.org/W2103767147","https://openalex.org/W2108651950","https://openalex.org/W2113151716","https://openalex.org/W2138317295","https://openalex.org/W2151460005","https://openalex.org/W2151980723","https://openalex.org/W2162853993","https://openalex.org/W2177114385","https://openalex.org/W4240109061","https://openalex.org/W4255339412","https://openalex.org/W4299430724"],"related_works":["https://openalex.org/W1508692582","https://openalex.org/W4289598248","https://openalex.org/W2044899742","https://openalex.org/W156527372","https://openalex.org/W2370399136","https://openalex.org/W2003652533","https://openalex.org/W2896088186","https://openalex.org/W2375103940","https://openalex.org/W2378716726","https://openalex.org/W1620410898"],"abstract_inverted_index":{"Abstract":[0],"This":[1,42],"paper":[2],"deals":[3],"with":[4],"the":[5,9,22,46,66,102,107],"stability":[6,63],"study":[7],"of":[8,39,48,65],"nonlinear":[10,50,67],"Saint-Venant":[11,68],"Partial":[12],"Differential":[13],"Equation":[14],"(PDE).":[15],"The":[16,87],"proposed":[17,71],"approach":[18],"is":[19,70,89],"based":[20],"on":[21],"multi-model":[23],"concept":[24],"which":[25],"takes":[26],"into":[27],"account":[28],"some":[29],"Linear":[30,75],"Time":[31],"Invariant":[32],"(LTI)":[33],"models":[34],"defined":[35],"around":[36],"a":[37,58,98],"set":[38],"operating":[40,60],"points.":[41],"method":[43,88],"allows":[44],"describing":[45],"dynamics":[47],"this":[49],"system":[51],"in":[52,92,106],"an":[53,80],"infinite":[54],"dimensional":[55],"space":[56],"over":[57],"wide":[59],"range.":[61],"A":[62],"analysis":[64],"PDE":[69],"both":[72,91],"by":[73],"using":[74],"Matrix":[76],"Inequalities":[77],"(LMIs)":[78],"and":[79,94],"Internal":[81],"Model":[82],"Boundary":[83],"Control":[84],"(IMBC)":[85],"structure.":[86],"applied":[90],"simulations":[93],"real":[95],"experiments":[96],"through":[97],"microchannel,":[99],"illustrating":[100],"thus":[101],"theoretical":[103],"results":[104],"developed":[105],"paper.":[108]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2016-06-24T00:00:00"}
