{"id":"https://openalex.org/W2075685426","doi":"https://doi.org/10.1137/s036301299833519x","title":"Optimizability and Estimatability for Infinite-Dimensional Linear Systems","display_name":"Optimizability and Estimatability for Infinite-Dimensional Linear Systems","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2075685426","doi":"https://doi.org/10.1137/s036301299833519x","mag":"2075685426"},"language":"en","primary_location":{"id":"doi:10.1137/s036301299833519x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s036301299833519x","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/A5003773351","display_name":"George H. Weiss","orcid":"https://orcid.org/0000-0002-9524-2795"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"George Weiss","raw_affiliation_strings":["Imperial College London,#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Imperial College London,#TAB#","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082625544","display_name":"Richard Rebarber","orcid":"https://orcid.org/0000-0001-7899-5683"},"institutions":[{"id":"https://openalex.org/I114395901","display_name":"University of Nebraska\u2013Lincoln","ror":"https://ror.org/043mer456","country_code":"US","type":"education","lineage":["https://openalex.org/I114395901"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard Rebarber","raw_affiliation_strings":["#N##TAB##TAB##TAB##TAB# University of Nebraska-Lincoln#N##TAB##TAB##TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"#N##TAB##TAB##TAB##TAB# University of Nebraska-Lincoln#N##TAB##TAB##TAB#","institution_ids":["https://openalex.org/I114395901"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.9787,"has_fulltext":false,"cited_by_count":79,"citation_normalized_percentile":{"value":0.97025138,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"39","issue":"4","first_page":"1204","last_page":"1232"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9700999855995178,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9584000110626221,"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/mathematics","display_name":"Mathematics","score":0.8495489358901978},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.6999362707138062},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6785447597503662},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.5842570066452026},{"id":"https://openalex.org/keywords/linear-map","display_name":"Linear map","score":0.5638294816017151},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5349323749542236},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.49756863713264465},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4735623598098755},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.4605187177658081},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.45858263969421387},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4492076337337494},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4364294707775116},{"id":"https://openalex.org/keywords/exponential-dichotomy","display_name":"Exponential dichotomy","score":0.43375590443611145},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4028118848800659},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3713024854660034},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.15519046783447266},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.0883077085018158},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07082653045654297}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8495489358901978},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.6999362707138062},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6785447597503662},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.5842570066452026},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.5638294816017151},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5349323749542236},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.49756863713264465},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4735623598098755},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.4605187177658081},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.45858263969421387},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4492076337337494},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4364294707775116},{"id":"https://openalex.org/C2779844894","wikidata":"https://www.wikidata.org/wiki/Q5421516","display_name":"Exponential dichotomy","level":3,"score":0.43375590443611145},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4028118848800659},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3713024854660034},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.15519046783447266},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0883077085018158},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07082653045654297},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s036301299833519x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s036301299833519x","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W33179366","https://openalex.org/W1495844786","https://openalex.org/W1538686203","https://openalex.org/W1591627731","https://openalex.org/W1595133563","https://openalex.org/W1929958170","https://openalex.org/W1978221522","https://openalex.org/W1981564132","https://openalex.org/W1985427687","https://openalex.org/W1986653700","https://openalex.org/W1991059830","https://openalex.org/W1992913239","https://openalex.org/W1997705656","https://openalex.org/W2002475330","https://openalex.org/W2004451407","https://openalex.org/W2021191412","https://openalex.org/W2022481994","https://openalex.org/W2025621348","https://openalex.org/W2028802911","https://openalex.org/W2029710005","https://openalex.org/W2030958501","https://openalex.org/W2031521898","https://openalex.org/W2032886082","https://openalex.org/W2041054619","https://openalex.org/W2049892514","https://openalex.org/W2053449213","https://openalex.org/W2066913295","https://openalex.org/W2068560252","https://openalex.org/W2076956178","https://openalex.org/W2077073668","https://openalex.org/W2091634205","https://openalex.org/W2093591297","https://openalex.org/W2097071461","https://openalex.org/W2134372275","https://openalex.org/W2156127866","https://openalex.org/W2165368325","https://openalex.org/W2170855688","https://openalex.org/W2173130135","https://openalex.org/W2178158283","https://openalex.org/W4236945040","https://openalex.org/W4250608538"],"related_works":["https://openalex.org/W3106150653","https://openalex.org/W1977278301","https://openalex.org/W2924465594","https://openalex.org/W4386136165","https://openalex.org/W2187202983","https://openalex.org/W2110739653","https://openalex.org/W3188606785","https://openalex.org/W2510347309","https://openalex.org/W2379495416","https://openalex.org/W99504509"],"abstract_inverted_index":{"An":[0],"infinite-dimensional":[1],"linear":[2,97],"system":[3,105,115],"described":[4],"by":[5,134],"$\\dot{x}(t)=Ax(t)+Bu(t)$":[6],"$(t\\geq":[7],"0)$":[8],"is":[9,33,47,106,116,124],"said":[10],"to":[11],"be":[12,25],"optimizable":[13,107],"if":[14,103,119,122],"for":[15,52],"every":[16],"initial":[17],"state":[18],"x(0),":[19],"an":[20,48],"input":[21],"$u\\in":[22],"L^2$":[23],"can":[24],"found":[26],"such":[27],"that":[28,112],"$x\\in":[29],"L^2$.":[30],"Here,":[31],"A":[32],"the":[34,64,74,87,99,104,132,146],"generator":[35],"of":[36,89,95],"a":[37,42,82,113,150],"strongly":[38],"continuous":[39],"semigroup":[40],"on":[41,138],"Hilbert":[43],"space":[44,144],"and":[45,68,78,92,108,120,127,149],"B":[46],"admissible":[49],"control":[50],"operator":[51],"this":[53,56],"semigroup.":[54],"In":[55],"paper":[57],"we":[58],"investigate":[59],"optimizability":[60],"(also":[61],"known":[62],"as":[63],"finite":[65],"cost":[66],"condition)":[67],"its":[69],"dual,":[70],"estimatability.":[71],"We":[72,80,110,130],"explore":[73],"connections":[75],"with":[76],"stabilizability":[77],"detectability.":[79],"give":[81],"very":[83],"general":[84],"theorem":[85],"about":[86],"equivalence":[88],"input-output":[90,128],"stability":[91,94],"exponential":[93],"well-posed":[96,114],"systems:":[98],"two":[100,135,141],"are":[101],"equivalent":[102],"estimatable.":[109],"conclude":[111],"exponentially":[117],"stable":[118],"only":[121],"it":[123],"dynamically":[125],"stabilizable":[126],"stable.":[129],"illustrate":[131],"theory":[133],"examples":[136],"based":[137],"PDEs":[139],"in":[140],"or":[142],"more":[143],"dimensions:":[145],"wave":[147],"equation":[148],"structural":[151],"acoustics":[152],"model.":[153]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
