{"id":"https://openalex.org/W4403674880","doi":"https://doi.org/10.1109/tac.2024.3485450","title":"A TBLMI Framework for Harmonic Robust Control","display_name":"A TBLMI Framework for Harmonic Robust Control","publication_year":2024,"publication_date":"2024-10-23","ids":{"openalex":"https://openalex.org/W4403674880","doi":"https://doi.org/10.1109/tac.2024.3485450"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2024.3485450","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2024.3485450","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-04273558","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112901546","display_name":"Flora Vernerey","orcid":"https://orcid.org/0009-0001-4382-6537"},"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/I4210110792","display_name":"Centre de Recherche en Automatique de Nancy","ror":"https://ror.org/022r5hc56","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210099203","https://openalex.org/I4210100260","https://openalex.org/I4210110792","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Flora Vernerey","raw_affiliation_strings":["CNRS, CRAN, Universit&#x00E9; de Lorraine, Nancy, France","Universit&#x00E9; de Lorraine, CNRS, CRAN, Nancy, France"],"raw_orcid":"https://orcid.org/0009-0001-4382-6537","affiliations":[{"raw_affiliation_string":"CNRS, CRAN, Universit&#x00E9; de Lorraine, Nancy, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210110792","https://openalex.org/I90183372"]},{"raw_affiliation_string":"Universit&#x00E9; de Lorraine, CNRS, CRAN, Nancy, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210110792","https://openalex.org/I90183372"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049970734","display_name":"Pierre Riedinger","orcid":"https://orcid.org/0000-0002-8221-4736"},"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/I4210110792","display_name":"Centre de Recherche en Automatique de Nancy","ror":"https://ror.org/022r5hc56","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210099203","https://openalex.org/I4210100260","https://openalex.org/I4210110792","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre Riedinger","raw_affiliation_strings":["CNRS, CRAN, Universit&#x00E9; de Lorraine, Nancy, France","Universit&#x00E9; de Lorraine, CNRS, CRAN, Nancy, France"],"raw_orcid":"https://orcid.org/0000-0002-8221-4736","affiliations":[{"raw_affiliation_string":"CNRS, CRAN, Universit&#x00E9; de Lorraine, Nancy, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210110792","https://openalex.org/I90183372"]},{"raw_affiliation_string":"Universit&#x00E9; de Lorraine, CNRS, CRAN, Nancy, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210110792","https://openalex.org/I90183372"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015675169","display_name":"Jamal Daafouz","orcid":"https://orcid.org/0000-0001-8313-8790"},"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/I4210110792","display_name":"Centre de Recherche en Automatique de Nancy","ror":"https://ror.org/022r5hc56","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210099203","https://openalex.org/I4210100260","https://openalex.org/I4210110792","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jamal Daafouz","raw_affiliation_strings":["CNRS, CRAN, Universit&#x00E9; de Lorraine, Nancy, France","Universit&#x00E9; de Lorraine, CNRS, CRAN, Nancy, France"],"raw_orcid":"https://orcid.org/0000-0001-8313-8790","affiliations":[{"raw_affiliation_string":"CNRS, CRAN, Universit&#x00E9; de Lorraine, Nancy, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210110792","https://openalex.org/I90183372"]},{"raw_affiliation_string":"Universit&#x00E9; de Lorraine, CNRS, CRAN, Nancy, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210110792","https://openalex.org/I90183372"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5592,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.62487587,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"70","issue":"4","first_page":"2537","last_page":"2551"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9904999732971191,"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/T11236","display_name":"Control Systems and Identification","score":0.9904999732971191,"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/T11372","display_name":"Hydraulic and Pneumatic Systems","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T11749","display_name":"Iterative Learning Control Systems","score":0.9628000259399414,"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/control-theory","display_name":"Control theory (sociology)","score":0.6365064382553101},{"id":"https://openalex.org/keywords/robust-control","display_name":"Robust control","score":0.5907623767852783},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.4449472427368164},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.4358159303665161},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4237043857574463},{"id":"https://openalex.org/keywords/harmonic-analysis","display_name":"Harmonic analysis","score":0.4209868311882019},{"id":"https://openalex.org/keywords/control-system","display_name":"Control system","score":0.37432289123535156},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.3568806052207947},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30654245615005493},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.21508434414863586},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1875632107257843},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11936086416244507},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.09893375635147095},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0953141450881958},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.08201047778129578}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6365064382553101},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.5907623767852783},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.4449472427368164},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4358159303665161},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4237043857574463},{"id":"https://openalex.org/C131770355","wikidata":"https://www.wikidata.org/wiki/Q876215","display_name":"Harmonic analysis","level":2,"score":0.4209868311882019},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.37432289123535156},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.3568806052207947},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30654245615005493},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.21508434414863586},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1875632107257843},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11936086416244507},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.09893375635147095},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0953141450881958},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.08201047778129578}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2024.3485450","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2024.3485450","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-04273558v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04273558","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, 2019, &#x27E8;10.1109/TAC.2024.3485450&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-04273558v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04273558","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, 2019, &#x27E8;10.1109/TAC.2024.3485450&#x27E9;","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.5400000214576721}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1995902921","https://openalex.org/W2002357820","https://openalex.org/W2014077309","https://openalex.org/W2022919271","https://openalex.org/W2028791438","https://openalex.org/W2048683800","https://openalex.org/W2066605554","https://openalex.org/W2078625090","https://openalex.org/W2079902511","https://openalex.org/W2093036603","https://openalex.org/W2117825464","https://openalex.org/W2130201778","https://openalex.org/W2139349731","https://openalex.org/W2140974698","https://openalex.org/W2154938264","https://openalex.org/W2165878769","https://openalex.org/W2170133674","https://openalex.org/W2291947042","https://openalex.org/W2963795895","https://openalex.org/W3011869242","https://openalex.org/W3120247183","https://openalex.org/W3210839039","https://openalex.org/W4210966175","https://openalex.org/W4283368224","https://openalex.org/W4327670913","https://openalex.org/W4381491225","https://openalex.org/W6634701477","https://openalex.org/W6712345869","https://openalex.org/W6741181457"],"related_works":["https://openalex.org/W2587667458","https://openalex.org/W2164070943","https://openalex.org/W2983963786","https://openalex.org/W1861882962","https://openalex.org/W1497667432","https://openalex.org/W2163128389","https://openalex.org/W2121926536","https://openalex.org/W1516921425","https://openalex.org/W2390836177","https://openalex.org/W2568904611"],"abstract_inverted_index":{"The":[0],"primary":[1],"objective":[2],"of":[3,35,44,57,65,162,187,194],"this":[4,50,93,177],"article":[5],"is":[6,133],"to":[7,12,53,79,92,97,142],"demonstrate":[8,191],"that":[9,74,89,129,190],"problems":[10],"related":[11],"stability":[13],"and":[14,115,167],"robust":[15],"control":[16,144],"in":[17,49],"the":[18,33,45,54,62,77,90,100,112,116,121,152,156,160,163,168,192],"harmonic":[19,113,157,164],"context":[20],"can":[21],"be":[22],"effectively":[23,75],"addressed":[24],"by":[25],"formulating":[26],"them":[27],"as":[28],"semidefinite":[29],"optimization":[30,83],"problems,":[31,67],"invoking":[32],"concept":[34],"infinite-dimensional":[36,59,101],"Toeplitz":[37,173],"block":[38,174],"linear":[39],"matrix":[40],"inequalities":[41],"(TBLMIs).":[42],"One":[43],"central":[46],"challenges":[47],"tackled":[48],"study":[51],"pertains":[52],"efficient":[55],"resolution":[56],"these":[58],"TBLMIs.":[60],"Exploiting":[61],"structured":[63],"nature":[64],"such":[66],"we":[68,87,107,150,179],"introduce":[69],"a":[70,80,109,185],"consistent":[71],"truncation":[72],"method":[73],"reduces":[76],"problem":[78,95],"finite-dimensional":[81,94],"convex":[82],"problem.":[84],"By":[85],"consistent,":[86],"mean":[88],"solution":[91,102],"allows":[96],"closely":[98],"approximate":[99],"with":[103,184],"arbitrary":[104],"precision.":[105],"Furthermore,":[106],"establish":[108],"link":[110],"between":[111],"framework":[114,132],"time":[117],"domain":[118],"setting,":[119],"emphasizing":[120],"advantages":[122],"over":[123],"periodic":[124],"differential":[125],"LMIs.":[126],"We":[127],"illustrate":[128],"our":[130,181,195],"proposed":[131],"not":[134],"only":[135],"theoretically":[136],"sound":[137],"but":[138],"also":[139],"practically":[140],"applicable":[141],"solving$H_{2}$and$H_\\infty$harmonic":[143],"design":[145],"problems.":[146],"To":[147],"enable":[148],"this,":[149],"extend":[151],"definitions":[153],"of$H_{2}$and$H_\\infty$norms":[154],"into":[155],"space,":[158],"leveraging":[159],"concepts":[161],"transfer":[165],"function":[166],"average":[169],"trace":[170],"operator":[171],"for":[172],"operators.":[175],"Throughout":[176],"article,":[178],"support":[180],"theoretical":[182],"contributions":[183],"range":[186],"illustrative":[188],"examples":[189],"effectiveness":[193],"approach.":[196]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
