{"id":"https://openalex.org/W2117870469","doi":"https://doi.org/10.1137/100790628","title":"Spectral Conditions Implied by Observability","display_name":"Spectral Conditions Implied by Observability","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2117870469","doi":"https://doi.org/10.1137/100790628","mag":"2117870469"},"language":"en","primary_location":{"id":"doi:10.1137/100790628","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100790628","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/A5081045551","display_name":"Fatima-Zahrae El Alaoui","orcid":"https://orcid.org/0000-0001-8912-4031"},"institutions":[{"id":"https://openalex.org/I1325784139","display_name":"Yahoo (United Kingdom)","ror":"https://ror.org/038p3gq39","country_code":"GB","type":"company","lineage":["https://openalex.org/I1325784139","https://openalex.org/I4210134091"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Fatima-Zahrae El Alaoui","raw_affiliation_strings":["fati3335@yahoo.fr and Boutouloutali@yahoo.fr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"fati3335@yahoo.fr and Boutouloutali@yahoo.fr#TAB#","institution_ids":["https://openalex.org/I1325784139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041102285","display_name":"Hans Zwart","orcid":"https://orcid.org/0000-0003-3451-7967"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hans Zwart","raw_affiliation_strings":["h.j.zwart@math.utwente.nl#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"h.j.zwart@math.utwente.nl#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054658066","display_name":"Ali Boutoulout","orcid":"https://orcid.org/0000-0003-4487-2946"},"institutions":[{"id":"https://openalex.org/I4210153608","display_name":"Universit\u00e9 Moulay Ismail de Meknes","ror":"https://ror.org/04cnscd67","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210153608"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Ali Boutoulout","raw_affiliation_strings":["Department of Mathematics and Computer Sciences, TSI Team, MACS Laboratory, Faculty of Sciences, Moulay Ismail University, B. P. 11201, Zitoune-Meknes, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Sciences, TSI Team, MACS Laboratory, Faculty of Sciences, Moulay Ismail University, B. P. 11201, Zitoune-Meknes, Morocco","institution_ids":["https://openalex.org/I4210153608"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3017,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.85234681,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"49","issue":"2","first_page":"672","last_page":"685"},"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":0.9997000098228455,"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":0.9997000098228455,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9836000204086304,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9708999991416931,"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/observability","display_name":"Observability","score":0.9713483452796936},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8322070837020874},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.6562726497650146},{"id":"https://openalex.org/keywords/infinitesimal","display_name":"Infinitesimal","score":0.5531585812568665},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.499920129776001},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.48447251319885254},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4318172335624695},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.42655065655708313},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42504674196243286},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.30394405126571655},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08055973052978516},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07136407494544983}],"concepts":[{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.9713483452796936},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8322070837020874},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.6562726497650146},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.5531585812568665},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.499920129776001},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.48447251319885254},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4318172335624695},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.42655065655708313},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42504674196243286},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.30394405126571655},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08055973052978516},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07136407494544983},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/100790628","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100790628","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:ris.utwente.nl:openaire/af340faf-4858-489f-b64a-a4c6564710f3","is_oa":false,"landing_page_url":"https://research.utwente.nl/en/publications/af340faf-4858-489f-b64a-a4c6564710f3","pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"El Alaoui, F-Z, Zwart, H J & Boutoulout, A 2011, 'Spectral conditions implied by observability', SIAM journal on control and optimization, vol. 49, no. 2, pp. 672-685. https://doi.org/10.1137/100790628","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:ris.utwente.nl:publications/af340faf-4858-489f-b64a-a4c6564710f3","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321015","display_name":"University of Twente","ror":"https://ror.org/006hf6230"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W152012262","https://openalex.org/W1999083650","https://openalex.org/W2007598313","https://openalex.org/W2017059115","https://openalex.org/W2017069511","https://openalex.org/W2029534953","https://openalex.org/W2036352409","https://openalex.org/W2041054619","https://openalex.org/W2047226152","https://openalex.org/W2068641177","https://openalex.org/W2082769641","https://openalex.org/W2083393007","https://openalex.org/W2085703760","https://openalex.org/W2087162566","https://openalex.org/W2093467872","https://openalex.org/W2093591297","https://openalex.org/W2116264516","https://openalex.org/W2135871258"],"related_works":["https://openalex.org/W2046459260","https://openalex.org/W2967463586","https://openalex.org/W2765830098","https://openalex.org/W1971989957","https://openalex.org/W2517338020","https://openalex.org/W3157641275","https://openalex.org/W4312300846","https://openalex.org/W2615757685","https://openalex.org/W11481024","https://openalex.org/W2015891994"],"abstract_inverted_index":{"It":[0],"is":[1,37,49,101,106],"well":[2],"known":[3],"that":[4,33,42,71,102],"a":[5],"finite-dimensional":[6],"output":[7,28,35],"space":[8],"implies":[9],"limitations":[10],"on":[11],"the":[12,31,34,47,55,58,83,91,104,110,114],"systems":[13],"properties,":[14],"like":[15],"observability":[16,79],"and":[17,46],"detectability.":[18],"In":[19],"this":[20,24,44,72,94,99],"paper":[21],"we":[22,69,86],"extend":[23],"result":[25,73,100],"for":[26,77,93],"infinite-dimensional":[27],"spaces,":[29],"under":[30],"condition":[32],"operator":[36],"relatively":[38],"compact.":[39,63],"We":[40],"show":[41,70],"if":[43,103],"holds,":[45],"system":[48,105],"exactly":[50],"observable":[51],"in":[52,80],"finite-time,":[53],"then":[54,109],"inverse":[56],"of":[57,66,90,98,113,117],"infinitesimal":[59],"generator":[60,92],"must":[61],"be":[62],"By":[64],"means":[65],"an":[67],"example":[68],"does":[74],"not":[75],"hold":[76],"exact":[78],"infinite-time.":[81],"Using":[82],"Hautus":[84],"test,":[85],"obtain":[87],"spectral":[88],"properties":[89],"case.":[95],"A":[96],"consequence":[97],"exponentially":[107],"detectable,":[108],"unstable":[111],"part":[112],"spectrum":[115,120],"consists":[116],"only":[118],"point":[119],"with":[121],"finite":[122],"multiplicity.":[123]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
