{"id":"https://openalex.org/W4321491620","doi":"https://doi.org/10.1137/22m1485139","title":"Observability for Non-autonomous Systems","display_name":"Observability for Non-autonomous Systems","publication_year":2023,"publication_date":"2023-02-22","ids":{"openalex":"https://openalex.org/W4321491620","doi":"https://doi.org/10.1137/22m1485139"},"language":"en","primary_location":{"id":"doi:10.1137/22m1485139","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1485139","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/A5056429222","display_name":"Clemens Bombach","orcid":null},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Clemens Bombach","raw_affiliation_strings":["Technische Universit\u00e4t Chemnitz, Fakult\u00e4t f\u00fcr Mathematik, D-09126 Chemnitz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Chemnitz, Fakult\u00e4t f\u00fcr Mathematik, D-09126 Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088862436","display_name":"Fabian Gabel","orcid":"https://orcid.org/0000-0002-8053-0284"},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Fabian Gabel","raw_affiliation_strings":["Technische Universit\u00e4t Hamburg, Institut f\u00fcr Mathematik, D-21073 Hamburg, Germany"],"raw_orcid":"https://orcid.org/0000-0002-8053-0284","affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Hamburg, Institut f\u00fcr Mathematik, D-21073 Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060280412","display_name":"Christian Seifert","orcid":"https://orcid.org/0000-0001-9182-8687"},"institutions":[{"id":"https://openalex.org/I32021983","display_name":"Christian-Albrechts-Universit\u00e4t zu Kiel","ror":"https://ror.org/04v76ef78","country_code":"DE","type":"education","lineage":["https://openalex.org/I32021983"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Seifert","raw_affiliation_strings":["Technische Universit\u00e4t Hamburg, Institut f\u00fcr Mathematik, Am Schwarzenberg-Campus 3, D-21073 Hamburg, Germany, and Christian-Albrechts-Universit\u00e4t zu Kiel, Mathematisches Seminar, D-24118 Kiel, Germany"],"raw_orcid":"https://orcid.org/0000-0001-9182-8687","affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Hamburg, Institut f\u00fcr Mathematik, Am Schwarzenberg-Campus 3, D-21073 Hamburg, Germany, and Christian-Albrechts-Universit\u00e4t zu Kiel, Mathematisches Seminar, D-24118 Kiel, Germany","institution_ids":["https://openalex.org/I32021983"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022960486","display_name":"Martin Tautenhahn","orcid":"https://orcid.org/0000-0002-6169-0493"},"institutions":[{"id":"https://openalex.org/I926574661","display_name":"Leipzig University","ror":"https://ror.org/03s7gtk40","country_code":"DE","type":"education","lineage":["https://openalex.org/I926574661"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Tautenhahn","raw_affiliation_strings":["Universit\u00e4t Leipzig, Mathematisches Institut, Augustusplatz 10, D-04109 Leipzig, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Leipzig, Mathematisches Institut, Augustusplatz 10, D-04109 Leipzig, Germany","institution_ids":["https://openalex.org/I926574661"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5163,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.62663082,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"61","issue":"1","first_page":"315","last_page":"341"},"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":0.9932000041007996,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/observability","display_name":"Observability","score":0.8911991119384766},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8024267554283142},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6873412728309631},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.686000406742096},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5756327509880066},{"id":"https://openalex.org/keywords/elliptic-operator","display_name":"Elliptic operator","score":0.5381193161010742},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5200154781341553},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.4324554204940796},{"id":"https://openalex.org/keywords/measurable-function","display_name":"Measurable function","score":0.42435771226882935},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41813158988952637},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4157186448574066},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3264073133468628},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.11022570729255676},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08231428265571594},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06929785013198853}],"concepts":[{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.8911991119384766},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8024267554283142},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6873412728309631},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.686000406742096},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5756327509880066},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.5381193161010742},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5200154781341553},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.4324554204940796},{"id":"https://openalex.org/C43994743","wikidata":"https://www.wikidata.org/wiki/Q516776","display_name":"Measurable function","level":3,"score":0.42435771226882935},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41813158988952637},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4157186448574066},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3264073133468628},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.11022570729255676},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08231428265571594},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06929785013198853},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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":1,"locations":[{"id":"doi:10.1137/22m1485139","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1485139","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":38,"referenced_works":["https://openalex.org/W1179366910","https://openalex.org/W1521738998","https://openalex.org/W1527296550","https://openalex.org/W1531371725","https://openalex.org/W1672092479","https://openalex.org/W1965657934","https://openalex.org/W1982510265","https://openalex.org/W1985812044","https://openalex.org/W2002744405","https://openalex.org/W2011483362","https://openalex.org/W2025256645","https://openalex.org/W2027753843","https://openalex.org/W2052105083","https://openalex.org/W2053445895","https://openalex.org/W2072395213","https://openalex.org/W2073592294","https://openalex.org/W2074865562","https://openalex.org/W2091017118","https://openalex.org/W2156795890","https://openalex.org/W2166161057","https://openalex.org/W2625273684","https://openalex.org/W2768980790","https://openalex.org/W2898906188","https://openalex.org/W2940020860","https://openalex.org/W2946255877","https://openalex.org/W2962712082","https://openalex.org/W2963321232","https://openalex.org/W2963810514","https://openalex.org/W2964134857","https://openalex.org/W2964225436","https://openalex.org/W3082126725","https://openalex.org/W3090335746","https://openalex.org/W3102271101","https://openalex.org/W3104605965","https://openalex.org/W3104811463","https://openalex.org/W4230442041","https://openalex.org/W4242473853","https://openalex.org/W4302061159"],"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/W2053863919","https://openalex.org/W3203168443"],"abstract_inverted_index":{"We":[0,83],"study":[1],"non-autonomous":[2,102,118],"observation":[3,41,64,109,139],"systems":[4],"\\begin{align*}":[5],"\\dot{x}(t)":[6],"=":[7,11,15,112],"A(t)":[8],"x(t),\\quad":[9,13],"y(t)":[10],"C(t)":[12],"x(0)":[14],"x_0\\in":[16],"X,":[17],"\\end{align*}":[18],"where":[19],"$(A(t))$":[20,92],"is":[21,36],"a":[22,30,37,46,57,67,142],"strongly":[23,95,119],"measurable":[24,75],"family":[25,38,131],"of":[26,39,86,93,117,132],"closed":[27],"operators":[28,42,98,104,110],"on":[29,51,106,129],"Banach":[31,47],"space":[32,48],"$X$":[33,44],"and":[34,56,125],"$(C(t))$":[35],"bounded":[40],"from":[43],"to":[45,90],"$Y$.":[49],"Based":[50],"an":[52],"abstract":[53],"uncertainty":[54],"principle":[55],"dissipation":[58],"estimate,":[59],"we":[60,122],"prove":[61],"that":[62,136],"the":[63,87,115,130,137],"system":[65,140],"satisfies":[66,141],"final-state":[68,143],"observability":[69,144],"estimate":[70],"in":[71],"$\\mathrm{L}^r(E;":[72],"Y)$":[73],"for":[74],"subsets":[76],"$E":[77],"\\subseteq":[78],"[0,T],":[79],"T":[80],">":[81],"0$.":[82],"present":[84],"applications":[85],"above":[88],"result":[89],"families":[91],"uniformly":[94],"elliptic":[96,120],"differential":[97],"as":[99,101],"well":[100],"Ornstein-Uhlenbeck":[103],"$P(t)$":[105],"$\\mathrm{L}^p(\\mathbb{R}^d)$":[107],"with":[108],"$C(t)u":[111],"u|_{\\Omega(t)}$.":[113],"In":[114],"setting":[116],"operators,":[121],"derive":[123],"necessary":[124],"sufficient":[126],"geometric":[127],"conditions":[128],"sets":[133],"$(\\Omega(t))$":[134],"such":[135],"corresponding":[138],"estimate.":[145]},"counts_by_year":[{"year":2023,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
