{"id":"https://openalex.org/W2064171090","doi":"https://doi.org/10.2478/v10006-012-0024-7","title":"A Lyapunov functional for a system with a time-varying delay","display_name":"A Lyapunov functional for a system with a time-varying delay","publication_year":2012,"publication_date":"2012-06-01","ids":{"openalex":"https://openalex.org/W2064171090","doi":"https://doi.org/10.2478/v10006-012-0024-7","mag":"2064171090"},"language":"en","primary_location":{"id":"doi:10.2478/v10006-012-0024-7","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-012-0024-7","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-012-0024-7","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/v10006-012-0024-7","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023873049","display_name":"J\u00f3zef Duda","orcid":"https://orcid.org/0000-0002-0156-4145"},"institutions":[{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"J\u00f3zef Duda","raw_affiliation_strings":["Department of Automatics AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Cracow, Poland","Department of Automatics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Cracow, Poland"],"affiliations":[{"raw_affiliation_string":"Department of Automatics AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Cracow, Poland","institution_ids":["https://openalex.org/I686019"]},{"raw_affiliation_string":"Department of Automatics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Cracow, Poland","institution_ids":["https://openalex.org/I686019"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023873049"],"corresponding_institution_ids":["https://openalex.org/I686019"],"apc_list":{"value":4080,"currency":"PLN","value_usd":1100},"apc_paid":{"value":4080,"currency":"PLN","value_usd":1100},"fwci":2.8352,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.91165012,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"22","issue":"2","first_page":"327","last_page":"337"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9990000128746033,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9990000128746033,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9927999973297119,"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/T13935","display_name":"Mathematical Control Systems and Analysis","score":0.9896000027656555,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6977205276489258},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.6611056327819824},{"id":"https://openalex.org/keywords/lyapunov-optimization","display_name":"Lyapunov optimization","score":0.5672901272773743},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5557375550270081},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.5482332706451416},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5162820219993591},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.5123053789138794},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4880613088607788},{"id":"https://openalex.org/keywords/lti-system-theory","display_name":"LTI system theory","score":0.48500439524650574},{"id":"https://openalex.org/keywords/functional-approach","display_name":"Functional approach","score":0.46966636180877686},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.41274234652519226},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.37044134736061096},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.369488388299942},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.22386416792869568},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1383320391178131},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11650350689888},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06242936849594116}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6977205276489258},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6611056327819824},{"id":"https://openalex.org/C101403955","wikidata":"https://www.wikidata.org/wiki/Q6707083","display_name":"Lyapunov optimization","level":5,"score":0.5672901272773743},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5557375550270081},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.5482332706451416},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5162820219993591},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.5123053789138794},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4880613088607788},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.48500439524650574},{"id":"https://openalex.org/C2777131603","wikidata":"https://www.wikidata.org/wiki/Q5508796","display_name":"Functional approach","level":2,"score":0.46966636180877686},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.41274234652519226},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.37044134736061096},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.369488388299942},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.22386416792869568},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1383320391178131},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11650350689888},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06242936849594116},{"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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C107457646","wikidata":"https://www.wikidata.org/wiki/Q207434","display_name":"Human\u2013computer interaction","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2478/v10006-012-0024-7","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-012-0024-7","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-012-0024-7","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:10.1.1.390.8043","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.390.8043","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/amc22/amc2227.pdf","raw_type":"text"},{"id":"pmh:oai:zbc.uz.zgora.pl:46984","is_oa":false,"landing_page_url":"https://zbc.uz.zgora.pl/dlibra/docmetadata?showContent=true&id=46984","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=paper&paper=615","raw_type":"artyku\u0142"}],"best_oa_location":{"id":"doi:10.2478/v10006-012-0024-7","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-012-0024-7","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-012-0024-7","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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2064171090.pdf","grobid_xml":"https://content.openalex.org/works/W2064171090.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1481961866","https://openalex.org/W1502089761","https://openalex.org/W1535516791","https://openalex.org/W1973991076","https://openalex.org/W1976105261","https://openalex.org/W1981140738","https://openalex.org/W1988041926","https://openalex.org/W1988098342","https://openalex.org/W1989399884","https://openalex.org/W2002045670","https://openalex.org/W2011034037","https://openalex.org/W2015615314","https://openalex.org/W2016655824","https://openalex.org/W2019968983","https://openalex.org/W2051079365","https://openalex.org/W2051591980","https://openalex.org/W2079618027","https://openalex.org/W2083857189","https://openalex.org/W2096307847","https://openalex.org/W2114885996","https://openalex.org/W2150715742","https://openalex.org/W2170222979","https://openalex.org/W2174411374","https://openalex.org/W6628658961"],"related_works":["https://openalex.org/W2383986032","https://openalex.org/W2534107666","https://openalex.org/W2349796700","https://openalex.org/W2118944249","https://openalex.org/W2979241488","https://openalex.org/W3194517843","https://openalex.org/W118344564","https://openalex.org/W2164487476","https://openalex.org/W1977987201","https://openalex.org/W2210722882"],"abstract_inverted_index":{"A":[0],"Lyapunov":[1,18,64],"functional":[2,19,31],"for":[3,20,34,59],"a":[4,7,13,17,21,38,42],"system":[5,24,36,51],"with":[6,25,37,41],"time-varying":[8,28,39],"delay":[9,40],"The":[10,30,53],"paper":[11],"presents":[12],"method":[14,55],"to":[15],"determine":[16],"linear":[22],"time-invariant":[23],"an":[26],"interval":[27],"delay.":[29],"is":[32,47],"constructed":[33],"the":[35,50,60,63],"given":[43],"time":[44],"derivative,":[45],"which":[46],"calculated":[48],"on":[49],"trajectory.":[52],"presented":[54],"gives":[56],"analytical":[57],"formulas":[58],"coefficients":[61],"of":[62],"functional.":[65]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}