{"id":"https://openalex.org/W2132323042","doi":"https://doi.org/10.2478/v10006-008-0018-7","title":"Approximate Controllability of Infinite Dimensional Systems of the n-th Order","display_name":"Approximate Controllability of Infinite Dimensional Systems of the n-th Order","publication_year":2008,"publication_date":"2008-06-01","ids":{"openalex":"https://openalex.org/W2132323042","doi":"https://doi.org/10.2478/v10006-008-0018-7","mag":"2132323042"},"language":"en","primary_location":{"id":"doi:10.2478/v10006-008-0018-7","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-008-0018-7","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-008-0018-7","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://sciendo.com/pdf/10.2478/v10006-008-0018-7","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073078474","display_name":"Jerzy S. Respondek","orcid":"https://orcid.org/0000-0001-5621-3783"},"institutions":[{"id":"https://openalex.org/I119004910","display_name":"Silesian University of Technology","ror":"https://ror.org/02dyjk442","country_code":"PL","type":"education","lineage":["https://openalex.org/I119004910"]},{"id":"https://openalex.org/I4210087266","display_name":"Institute of Computer Science","ror":"https://ror.org/003fvp964","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210087266","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Jerzy Respondek","raw_affiliation_strings":["Institute of Computer Science Silesian University of Technology, ul. Akademicka 16, 44-100 Gliwice, Poland","Institute of Computer Science, Silesian University of Technology, ul. Akademicka 16, 44-100 Gliwice, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science Silesian University of Technology, ul. Akademicka 16, 44-100 Gliwice, Poland","institution_ids":["https://openalex.org/I119004910","https://openalex.org/I4210087266"]},{"raw_affiliation_string":"Institute of Computer Science, Silesian University of Technology, ul. Akademicka 16, 44-100 Gliwice, Poland","institution_ids":["https://openalex.org/I119004910","https://openalex.org/I4210087266"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073078474"],"corresponding_institution_ids":["https://openalex.org/I119004910","https://openalex.org/I4210087266"],"apc_list":{"value":4080,"currency":"PLN","value_usd":1100},"apc_paid":{"value":4080,"currency":"PLN","value_usd":1100},"fwci":14.9011,"has_fulltext":true,"cited_by_count":27,"citation_normalized_percentile":{"value":0.98921,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"18","issue":"2","first_page":"199","last_page":"212"},"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":0.9987999796867371,"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":0.9987999796867371,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"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":0.9976999759674072,"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/controllability","display_name":"Controllability","score":0.9646443128585815},{"id":"https://openalex.org/keywords/vandermonde-matrix","display_name":"Vandermonde matrix","score":0.8497859239578247},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7346236705780029},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6367753744125366},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5787020921707153},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5782509446144104},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5034131407737732},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4399038553237915},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3053051829338074},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.06771934032440186}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.9646443128585815},{"id":"https://openalex.org/C55294529","wikidata":"https://www.wikidata.org/wiki/Q579544","display_name":"Vandermonde matrix","level":3,"score":0.8497859239578247},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7346236705780029},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6367753744125366},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5787020921707153},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5782509446144104},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5034131407737732},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4399038553237915},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3053051829338074},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.06771934032440186},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2478/v10006-008-0018-7","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-008-0018-7","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-008-0018-7","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.390.2899","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.390.2899","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://matwbn.icm.edu.pl/ksiazki/amc/amc18/amc1828.pdf","raw_type":"text"},{"id":"pmh:oai:zbc.uz.zgora.pl:78709","is_oa":false,"landing_page_url":"https://zbc.uz.zgora.pl/dlibra/docmetadata?showContent=true&id=78709","pdf_url":null,"source":{"id":"https://openalex.org/S4306400400","display_name":"Digital library of Zielona Gora (University of Zielona G\u00f3ra)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I46305939","host_organization_name":"University of Zielona G\u00f3ra","host_organization_lineage":["https://openalex.org/I46305939"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.amcs.uz.zgora.pl/?action=papers&issue=32","raw_type":"artyku\u0142"}],"best_oa_location":{"id":"doi:10.2478/v10006-008-0018-7","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-008-0018-7","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-008-0018-7","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321042","display_name":"Fundacja na rzecz Nauki Polskiej","ror":"https://ror.org/048zd9m77"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2132323042.pdf","grobid_xml":"https://content.openalex.org/works/W2132323042.grobid-xml"},"referenced_works_count":55,"referenced_works":["https://openalex.org/W97416413","https://openalex.org/W218580582","https://openalex.org/W251890296","https://openalex.org/W588884542","https://openalex.org/W836987777","https://openalex.org/W1502696358","https://openalex.org/W1520090149","https://openalex.org/W1535516791","https://openalex.org/W1535905504","https://openalex.org/W1538686203","https://openalex.org/W1565738440","https://openalex.org/W1967467445","https://openalex.org/W1968010891","https://openalex.org/W1976978073","https://openalex.org/W1982510265","https://openalex.org/W1987382717","https://openalex.org/W1993663047","https://openalex.org/W1994972123","https://openalex.org/W1996378040","https://openalex.org/W1996887999","https://openalex.org/W2003383342","https://openalex.org/W2006977894","https://openalex.org/W2015567437","https://openalex.org/W2019955665","https://openalex.org/W2020977969","https://openalex.org/W2023940093","https://openalex.org/W2027026739","https://openalex.org/W2029221561","https://openalex.org/W2030793109","https://openalex.org/W2031389269","https://openalex.org/W2038267869","https://openalex.org/W2054901219","https://openalex.org/W2057419909","https://openalex.org/W2059493338","https://openalex.org/W2063164699","https://openalex.org/W2063973166","https://openalex.org/W2065272780","https://openalex.org/W2076629586","https://openalex.org/W2085719835","https://openalex.org/W2089219998","https://openalex.org/W2095095978","https://openalex.org/W2121776795","https://openalex.org/W2122126503","https://openalex.org/W2130606767","https://openalex.org/W2135812273","https://openalex.org/W2146602316","https://openalex.org/W2166987719","https://openalex.org/W2179347143","https://openalex.org/W2490967256","https://openalex.org/W2798556646","https://openalex.org/W2887053799","https://openalex.org/W4250589534","https://openalex.org/W4362192038","https://openalex.org/W6653780080","https://openalex.org/W7036079001"],"related_works":["https://openalex.org/W2394313973","https://openalex.org/W1258664604","https://openalex.org/W4285223790","https://openalex.org/W2952052090","https://openalex.org/W4293585078","https://openalex.org/W2389636997","https://openalex.org/W2349018871","https://openalex.org/W2080915594","https://openalex.org/W3046922746","https://openalex.org/W3161838140"],"abstract_inverted_index":{"Approximate":[0],"Controllability":[1],"of":[2,6,13,24,33,37,68,80,83,104,120,145,149],"Infinite":[3],"Dimensional":[4],"Systems":[5],"the":[7,14,52,59,69,75,78,81,93,100,105,127,131,143,150],"n":[8,53],"-th":[9,54],"Order":[10],"The":[11,135],"objective":[12],"article":[15],"is":[16],"to":[17,50,90,112,142],"obtain":[18,113],"general":[19,115],"conditions":[20,38,116,128],"for":[21,28,39,117,122],"several":[22],"types":[23,119],"controllability":[25,94,121],"at":[26],"once":[27],"an":[29],"abstract":[30],"differential":[31],"equation":[32],"arbitrary":[34],"order,":[35],"instead":[36],"a":[40,64,84],"fixed":[41],"order":[42,55],"equation.":[43],"This":[44,109],"innovative":[45],"approach":[46],"was":[47],"possible":[48],"owing":[49],"analyzing":[51],"linear":[56],"system":[57],"in":[58,130],"Frobenius":[60],"form":[61,103],"which":[62],"generates":[63],"Jordan":[65,85],"transition":[66,86],"matrix":[67,87],"Vandermonde":[70,107],"form.":[71],"We":[72,98],"extensively":[73],"used":[74,99],"fact":[76],"that":[77],"knowledge":[79],"inverse":[82,106],"enables":[88],"us":[89,111],"directly":[91],"verify":[92],"by":[95],"Chen's":[96],"theorem.":[97],"explicit":[101],"analytical":[102],"matrix.":[108],"enabled":[110],"more":[114],"different":[118],"infinite":[123],"dimensional":[124],"systems":[125,151],"than":[126],"existing":[129],"literature":[132],"so":[133],"far.":[134],"methods":[136],"introduced":[137],"can":[138],"be":[139],"easily":[140],"adapted":[141],"analysis":[144],"other":[146],"dynamic":[147],"properties":[148],"considered.":[152]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}