{"id":"https://openalex.org/W2082801151","doi":"https://doi.org/10.1137/s036301290444349x","title":"Robust Matrix Root-Clustering Analysis through Extended KYP Lemma","display_name":"Robust Matrix Root-Clustering Analysis through Extended KYP Lemma","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2082801151","doi":"https://doi.org/10.1137/s036301290444349x","mag":"2082801151"},"language":"en","primary_location":{"id":"doi:10.1137/s036301290444349x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s036301290444349x","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-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/A5033272751","display_name":"Olivier Bachelier","orcid":"https://orcid.org/0000-0002-1655-891X"},"institutions":[{"id":"https://openalex.org/I4210116740","display_name":"Laboratoire d'Informatique et d'Automatique pour les Syst\u00e8mes","ror":"https://ror.org/02b5vq778","country_code":"FR","type":"facility","lineage":["https://openalex.org/I32881790","https://openalex.org/I4210116740"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Olivier Bachelier","raw_affiliation_strings":["LAII [Poitiers] - Laboratoire d'automatique et d'informatique industrielle [EA 1219] (40 avenue du recteur Pineau, 86022 Poitiers - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LAII [Poitiers] - Laboratoire d'automatique et d'informatique industrielle [EA 1219] (40 avenue du recteur Pineau, 86022 Poitiers - France)","institution_ids":["https://openalex.org/I4210116740"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012039416","display_name":"Driss Mehdi","orcid":"https://orcid.org/0000-0002-0045-7364"},"institutions":[{"id":"https://openalex.org/I4210116740","display_name":"Laboratoire d'Informatique et d'Automatique pour les Syst\u00e8mes","ror":"https://ror.org/02b5vq778","country_code":"FR","type":"facility","lineage":["https://openalex.org/I32881790","https://openalex.org/I4210116740"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Driss Mehdi","raw_affiliation_strings":["LAII [Poitiers] - Laboratoire d'automatique et d'informatique industrielle [EA 1219] (40 avenue du recteur Pineau, 86022 Poitiers - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LAII [Poitiers] - Laboratoire d'automatique et d'informatique industrielle [EA 1219] (40 avenue du recteur Pineau, 86022 Poitiers - France)","institution_ids":["https://openalex.org/I4210116740"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210116740"],"apc_list":null,"apc_paid":null,"fwci":0.8287,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.74999185,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"45","issue":"1","first_page":"368","last_page":"381"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9860000014305115,"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"}},{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9854999780654907,"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/mathematics","display_name":"Mathematics","score":0.8107197284698486},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.7072242498397827},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5801592469215393},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5668612122535706},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.5391237139701843},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.5335913896560669},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5266183018684387},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5226078629493713},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4579876661300659},{"id":"https://openalex.org/keywords/complex-matrix","display_name":"Complex matrix","score":0.4266735911369324},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3770860433578491},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3214527368545532},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2710736095905304}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8107197284698486},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.7072242498397827},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5801592469215393},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5668612122535706},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.5391237139701843},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.5335913896560669},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5266183018684387},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5226078629493713},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4579876661300659},{"id":"https://openalex.org/C2988629283","wikidata":"https://www.wikidata.org/wiki/Q44337","display_name":"Complex matrix","level":2,"score":0.4266735911369324},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3770860433578491},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3214527368545532},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2710736095905304},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s036301290444349x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s036301290444349x","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03273837v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03273837","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":"SIAM Journal on Control and Optimization, 2006, 45 (1), pp.368--381. &#x27E8;10.1137/S036301290444349X&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W816406765","https://openalex.org/W1547135986","https://openalex.org/W1972848510","https://openalex.org/W1976286176","https://openalex.org/W1994873143","https://openalex.org/W2000990668","https://openalex.org/W2002357820","https://openalex.org/W2012336502","https://openalex.org/W2034539682","https://openalex.org/W2036767392","https://openalex.org/W2039867272","https://openalex.org/W2046473141","https://openalex.org/W2050649877","https://openalex.org/W2051114549","https://openalex.org/W2055319245","https://openalex.org/W2059507126","https://openalex.org/W2061242746","https://openalex.org/W2075291379","https://openalex.org/W2077418568","https://openalex.org/W2080153087","https://openalex.org/W2091011675","https://openalex.org/W2094973444","https://openalex.org/W2108489060","https://openalex.org/W2118349044","https://openalex.org/W2125190651","https://openalex.org/W2171222770","https://openalex.org/W2172289902","https://openalex.org/W2417903161","https://openalex.org/W3210839039","https://openalex.org/W4252717076"],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1097487277","https://openalex.org/W2059548897","https://openalex.org/W2980803603","https://openalex.org/W3120086473","https://openalex.org/W2478408719","https://openalex.org/W2543799588","https://openalex.org/W2016923830","https://openalex.org/W2131967299","https://openalex.org/W1979998365"],"abstract_inverted_index":{"This":[0,37,47],"paper":[1,55,73],"is":[2,21,24,90],"dedicated":[3],"to":[4,64,75,80],"robust":[5],"matrix":[6],"eigenvalue":[7],"clustering":[8],"in":[9,52],"a":[10,53],"subregion":[11],"${\\mathcal":[12],"D}$":[13],"of":[14,29,35,84],"the":[15,42,57,68,85,93],"complex":[16,44],"plane.":[17],"A":[18],"norm-bounded":[19],"uncertainty":[20],"considered.":[22],"$\\cD$":[23],"any":[25],"intersection":[26],"and/or":[27],"union":[28],"half":[30],"planes,":[31],"discs,":[32],"and":[33],"outsides":[34],"discs.":[36],"work":[38],"aims":[39],"at":[40],"computing":[41],"associated":[43],"$\\cD$-stability":[45],"radius.":[46],"challenge":[48],"was":[49],"already":[50],"tackled":[51],"recent":[54],"but":[56],"technique":[58],"therein":[59],"may":[60],"fail":[61],"or":[62],"lead":[63],"conservative":[65],"results":[66],"when":[67],"subregions":[69],"overlap.":[70],"The":[71],"present":[72],"proposes":[74],"circumvent":[76],"those":[77],"limits":[78],"thanks":[79],"an":[81],"extended":[82],"version":[83],"Kalman-Yakubovich-Popov":[86],"(KYP)":[87],"lemma":[88],"which":[89],"deduced":[91],"from":[92],"so-called":[94],"generalized":[95],"S-procedure.":[96]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
