{"id":"https://openalex.org/W4386464493","doi":"https://doi.org/10.1109/cdc49753.2023.10383213","title":"Frequency domain approach for the stability analysis of a fast hyperbolic PDE coupled with a slow ODE","display_name":"Frequency domain approach for the stability analysis of a fast hyperbolic PDE coupled with a slow ODE","publication_year":2023,"publication_date":"2023-12-13","ids":{"openalex":"https://openalex.org/W4386464493","doi":"https://doi.org/10.1109/cdc49753.2023.10383213"},"language":"en","primary_location":{"id":"doi:10.1109/cdc49753.2023.10383213","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc49753.2023.10383213","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-04059956v2/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001609769","display_name":"Gonzalo Tejerina Arias","orcid":null},"institutions":[{"id":"https://openalex.org/I162148367","display_name":"Pontificia Universidad Cat\u00f3lica de Chile","ror":"https://ror.org/04teye511","country_code":"CL","type":"education","lineage":["https://openalex.org/I162148367"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Gonzalo Arias","raw_affiliation_strings":["Pontificia Universidad Cat&#x00F3;lica de Chile, Avda. Vicu&#x00F1;a Mackenna 4860, Macul,Santiago,Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Pontificia Universidad Cat&#x00F3;lica de Chile, Avda. Vicu&#x00F1;a Mackenna 4860, Macul,Santiago,Chile","institution_ids":["https://openalex.org/I162148367"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043449102","display_name":"Swann Marx","orcid":"https://orcid.org/0000-0002-0722-3560"},"institutions":[{"id":"https://openalex.org/I100445878","display_name":"\u00c9cole Centrale de Nantes","ror":"https://ror.org/03nh7d505","country_code":"FR","type":"education","lineage":["https://openalex.org/I100445878","https://openalex.org/I97188460"]},{"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/I4210117005","display_name":"Laboratoire des Sciences du Num\u00e9rique de Nantes","ror":"https://ror.org/02snf8m58","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100445878","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I205703379","https://openalex.org/I4210117005","https://openalex.org/I4210124215","https://openalex.org/I4210127572","https://openalex.org/I4210139971","https://openalex.org/I97188460","https://openalex.org/I97188460"]},{"id":"https://openalex.org/I97188460","display_name":"Nantes Universit\u00e9","ror":"https://ror.org/03gnr7b55","country_code":"FR","type":"education","lineage":["https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Swann Marx","raw_affiliation_strings":["Swann Marx is with LS2N, &#x00C9;cole Centrale de Nantes &#x0026; CNRS UMR 6004,Nantes,France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Swann Marx is with LS2N, &#x00C9;cole Centrale de Nantes &#x0026; CNRS UMR 6004,Nantes,France","institution_ids":["https://openalex.org/I97188460","https://openalex.org/I100445878","https://openalex.org/I4210117005","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066218521","display_name":"Guilherme Mazanti","orcid":"https://orcid.org/0000-0002-9197-0277"},"institutions":[{"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/I4210097418","display_name":"Laboratoire des signaux et syst\u00e8mes","ror":"https://ror.org/00skw9v43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Guilherme Mazanti","raw_affiliation_strings":["Guilherme Mazanti is with Universit&#x00E9; Paris-Saclay, CNRS, Centrale-Sup&#x00E9;lec, Inria,Laboratoire des signaux et syst&#x00E9;mes,Gif-sur-Yvette,France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Guilherme Mazanti is with Universit&#x00E9; Paris-Saclay, CNRS, Centrale-Sup&#x00E9;lec, Inria,Laboratoire des signaux et syst&#x00E9;mes,Gif-sur-Yvette,France","institution_ids":["https://openalex.org/I4210097418","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8237,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.72799551,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"1949","last_page":"1954"},"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":0.9994000196456909,"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":0.9994000196456909,"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":0.9983000159263611,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9958999752998352,"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/ode","display_name":"Ode","score":0.8875075578689575},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5801838636398315},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5688666105270386},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5574884414672852},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5356257557868958},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.504660964012146},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4954873323440552},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4771261215209961},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.46895116567611694},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4634399712085724},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4160258173942566},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27439162135124207},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.20941677689552307},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1007380485534668}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.8875075578689575},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5801838636398315},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5688666105270386},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5574884414672852},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5356257557868958},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.504660964012146},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4954873323440552},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4771261215209961},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.46895116567611694},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4634399712085724},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4160258173942566},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27439162135124207},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.20941677689552307},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1007380485534668},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc49753.2023.10383213","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc49753.2023.10383213","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-04059956v2","is_oa":true,"landing_page_url":"https://hal.science/hal-04059956","pdf_url":"https://hal.science/hal-04059956v2/document","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":"62nd IEEE Conference on Decision and Control, IEEE Control Systems Society (CSS), Dec 2023, Singapore, Singapore. pp.1949-1954, &#x27E8;10.1109/cdc49753.2023.10383213&#x27E9;","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-04059956v2","is_oa":true,"landing_page_url":"https://hal.science/hal-04059956","pdf_url":"https://hal.science/hal-04059956v2/document","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":"62nd IEEE Conference on Decision and Control, IEEE Control Systems Society (CSS), Dec 2023, Singapore, Singapore. pp.1949-1954, &#x27E8;10.1109/cdc49753.2023.10383213&#x27E9;","raw_type":"info:eu-repo/semantics/conferenceObject"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.4099999964237213,"id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G2373457110","display_name":null,"funder_award_id":"NCN19-161","funder_id":"https://openalex.org/F4320331146","funder_display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo"}],"funders":[{"id":"https://openalex.org/F4320331146","display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4386464493.pdf"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W66060913","https://openalex.org/W1515224583","https://openalex.org/W1982830050","https://openalex.org/W1984658683","https://openalex.org/W2018160219","https://openalex.org/W2022479657","https://openalex.org/W2057432879","https://openalex.org/W2120281474","https://openalex.org/W2238655651","https://openalex.org/W2482021336","https://openalex.org/W2740763313","https://openalex.org/W2780413159","https://openalex.org/W2928782170","https://openalex.org/W2979078298","https://openalex.org/W2995186665","https://openalex.org/W3099658790","https://openalex.org/W3100828148","https://openalex.org/W4211202937","https://openalex.org/W4311570730","https://openalex.org/W4313334987","https://openalex.org/W6846874482"],"related_works":["https://openalex.org/W3082668976","https://openalex.org/W2517973022","https://openalex.org/W1543121148","https://openalex.org/W1580703421","https://openalex.org/W2618518959","https://openalex.org/W2231364979","https://openalex.org/W4295745414","https://openalex.org/W4382202915","https://openalex.org/W4288093367","https://openalex.org/W3093456297"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3,15,18],"the":[4,22,25,33,51,55,63,78,81,85,99,102,105,116,120,127,148,160,175,180],"exponential":[5],"stability":[6,59],"of":[7,10,24,32,38,80,101,147],"systems":[8,122,149],"made":[9],"a":[11,36,44,73,94,144,156,166,171],"hyperbolic":[12],"PDE":[13,26,103],"coupled":[14],"an":[16],"ODE":[17],"different":[19],"time":[20,39,52,107],"scales,":[21],"dynamics":[23,79,100],"being":[27],"much":[28],"faster":[29],"than":[30],"that":[31],"ODE.":[34],"Such":[35],"difference":[37],"scales":[40],"is":[41,130,141],"modeled":[42],"though":[43],"small":[45,136],"parameter":[46],"<tex":[47,87],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[48,88],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\varepsilon$</tex>":[49],"multiplying":[50],"derivative":[53],"in":[54,84,104,159],"PDE,":[56],"and":[57,93,119,138,169],"our":[58,139],"analysis":[60,146],"relies":[61],"on":[62,143,174],"singular":[64],"perturbation":[65],"method.":[66],"More":[67],"precisely,":[68],"we":[69],"define":[70],"two":[71],"subsystems:":[72],"reduced":[74,117],"order":[75,118],"system,":[76,96],"representing":[77],"full":[82,128],"system":[83,129,177],"limit":[86],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\varepsilon":[89],"=":[90],"0$</tex>":[91],",":[92],"boundary-layer":[95,121,176],"which":[97,162],"represents":[98],"fast":[106],"scale.":[108],"Our":[109,152],"main":[110,153],"result":[111,154,158],"shows":[112],"that,":[113],"if":[114],"both":[115],"are":[123],"exponentially":[124,132],"stable,":[125],"then":[126],"also":[131],"stable":[133],"for":[134],"\u03b5":[135],"enough,":[137],"strategy":[140],"based":[142],"spectral":[145],"under":[150],"consideration.":[151],"improves":[155],"previous":[157],"literature,":[161],"was":[163],"proved":[164],"using":[165],"Lyapunov":[167],"approach":[168],"required":[170],"stronger":[172],"assumption":[173],"to":[178],"obtain":[179],"same":[181],"conclusion.":[182]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}