{"id":"https://openalex.org/W2082158625","doi":"https://doi.org/10.1080/00207170903171348","title":"Approximate controllability of impulsive differential equations with state-dependent delay","display_name":"Approximate controllability of impulsive differential equations with state-dependent delay","publication_year":2009,"publication_date":"2009-10-31","ids":{"openalex":"https://openalex.org/W2082158625","doi":"https://doi.org/10.1080/00207170903171348","mag":"2082158625"},"language":"en","primary_location":{"id":"doi:10.1080/00207170903171348","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170903171348","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","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/A5076621570","display_name":"R. Sakthivel","orcid":"https://orcid.org/0000-0002-5528-2709"},"institutions":[{"id":"https://openalex.org/I848706","display_name":"Sungkyunkwan University","ror":"https://ror.org/04q78tk20","country_code":"KR","type":"education","lineage":["https://openalex.org/I848706"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"R. Sakthivel","raw_affiliation_strings":["Department of Mathematics , Sungkyunkwan University , Suwon 440-746, South Korea","Department of Mathematics, SungKyunKwan University, Suwon 440-746, South Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Sungkyunkwan University , Suwon 440-746, South Korea","institution_ids":["https://openalex.org/I848706"]},{"raw_affiliation_string":"Department of Mathematics, SungKyunKwan University, Suwon 440-746, South Korea","institution_ids":["https://openalex.org/I848706"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021593404","display_name":"E. R. Anandhi","orcid":null},"institutions":[{"id":"https://openalex.org/I153297377","display_name":"Medical University of South Carolina","ror":"https://ror.org/012jban78","country_code":"US","type":"education","lineage":["https://openalex.org/I153297377"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"E.R. Anandhi","raw_affiliation_strings":["Department of Biostatistics , Medical University of South Carolina , Charleston, SC 29425, USA","Department of Biostatistics, Medical University of South Carolina, Charleston, SC 29425 USA"],"affiliations":[{"raw_affiliation_string":"Department of Biostatistics , Medical University of South Carolina , Charleston, SC 29425, USA","institution_ids":["https://openalex.org/I153297377"]},{"raw_affiliation_string":"Department of Biostatistics, Medical University of South Carolina, Charleston, SC 29425 USA","institution_ids":["https://openalex.org/I153297377"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5076621570"],"corresponding_institution_ids":["https://openalex.org/I848706"],"apc_list":null,"apc_paid":null,"fwci":6.0626,"has_fulltext":false,"cited_by_count":94,"citation_normalized_percentile":{"value":0.97019868,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"83","issue":"2","first_page":"387","last_page":"393"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9993000030517578,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.88479083776474},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7159661650657654},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.6656281352043152},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6204587817192078},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5437686443328857},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.508660614490509},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5013365745544434},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.501232385635376},{"id":"https://openalex.org/keywords/distributed-parameter-system","display_name":"Distributed parameter system","score":0.4863782227039337},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.43748271465301514},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3718656599521637},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1865711808204651},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1733950972557068},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0830484926700592},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.0614456832408905}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.88479083776474},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7159661650657654},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.6656281352043152},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6204587817192078},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5437686443328857},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.508660614490509},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5013365745544434},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.501232385635376},{"id":"https://openalex.org/C112714845","wikidata":"https://www.wikidata.org/wiki/Q1482001","display_name":"Distributed parameter system","level":3,"score":0.4863782227039337},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.43748271465301514},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3718656599521637},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1865711808204651},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1733950972557068},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0830484926700592},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0614456832408905},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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:10.1080/00207170903171348","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170903171348","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","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":25,"referenced_works":["https://openalex.org/W193221123","https://openalex.org/W1536762869","https://openalex.org/W1965618873","https://openalex.org/W1979983597","https://openalex.org/W1984958826","https://openalex.org/W1989117449","https://openalex.org/W2003540088","https://openalex.org/W2009071420","https://openalex.org/W2010522586","https://openalex.org/W2012592205","https://openalex.org/W2016841018","https://openalex.org/W2017869389","https://openalex.org/W2027177136","https://openalex.org/W2043506431","https://openalex.org/W2045826921","https://openalex.org/W2046414502","https://openalex.org/W2054855081","https://openalex.org/W2065111801","https://openalex.org/W2075054200","https://openalex.org/W2081182561","https://openalex.org/W2090058137","https://openalex.org/W2106544565","https://openalex.org/W2161475106","https://openalex.org/W2461092246","https://openalex.org/W4366819356"],"related_works":["https://openalex.org/W1976978073","https://openalex.org/W2332806069","https://openalex.org/W2325297408","https://openalex.org/W1484584348","https://openalex.org/W2187482192","https://openalex.org/W2152487891","https://openalex.org/W3105466232","https://openalex.org/W1994993030","https://openalex.org/W3195236465","https://openalex.org/W2111253939"],"abstract_inverted_index":{"In":[0,34],"order":[1],"to":[2,13,29,93],"describe":[3,30],"various":[4],"real-world":[5],"problems":[6],"in":[7],"physical":[8],"and":[9,79,86],"engineering":[10],"sciences":[11],"subject":[12],"abrupt":[14],"changes":[15],"at":[16],"certain":[17],"instants":[18],"during":[19],"the":[20,31,37,54,63,66,95],"evolution":[21],"process,":[22],"impulsive":[23,44,59],"differential":[24,45,60],"equations":[25,46],"have":[26],"been":[27],"used":[28],"system":[32,61,70],"model.":[33],"this":[35],"article,":[36],"problem":[38],"of":[39,76],"approximate":[40,55],"controllability":[41,56],"for":[42,57],"nonlinear":[43,58],"with":[47],"state-dependent":[48],"delay":[49],"is":[50,71,91],"investigated.":[51],"We":[52],"study":[53],"under":[62],"assumption":[64],"that":[65],"corresponding":[67],"linear":[68],"control":[69],"approximately":[72],"controllable.":[73],"Using":[74],"methods":[75],"functional":[77],"analysis":[78],"semigroup":[80],"theory,":[81],"sufficient":[82],"conditions":[83],"are":[84],"formulated":[85],"proved.":[87],"Finally,":[88],"an":[89],"example":[90],"provided":[92],"illustrate":[94],"proposed":[96],"theory.":[97]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":7}],"updated_date":"2026-03-06T13:50:29.536080","created_date":"2025-10-10T00:00:00"}