{"id":"https://openalex.org/W1966164211","doi":"https://doi.org/10.2478/v10006-012-0025-6","title":"LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties","display_name":"LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties","publication_year":2012,"publication_date":"2012-06-01","ids":{"openalex":"https://openalex.org/W1966164211","doi":"https://doi.org/10.2478/v10006-012-0025-6","mag":"1966164211"},"language":"en","primary_location":{"id":"doi:10.2478/v10006-012-0025-6","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-012-0025-6","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-012-0025-6","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/v10006-012-0025-6","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015256521","display_name":"P. Balasubramaniam","orcid":"https://orcid.org/0000-0001-9673-5949"},"institutions":[{"id":"https://openalex.org/I880551032","display_name":"Gandhigram Rural Institute","ror":"https://ror.org/01abtgj51","country_code":"IN","type":"education","lineage":["https://openalex.org/I880551032"]},{"id":"https://openalex.org/I111575329","display_name":"Bharathiar University","ror":"https://ror.org/04fht8c22","country_code":"IN","type":"education","lineage":["https://openalex.org/I111575329"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Pagavathigounder Balasubramaniam","raw_affiliation_strings":["Department of Mathematics Bharathiar University, Coimbatore 641 046, Tamilnadu, India","Department of Mathematics Gandhigram Rural Institute-Deemed University, Gandhigram 624 302, Tamilnadu, India","Department of Mathematics, Gandhigram Rural Institute ? Deemed University, Gandhigram-624 302, Tamilnadu, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Bharathiar University, Coimbatore 641 046, Tamilnadu, India","institution_ids":["https://openalex.org/I111575329"]},{"raw_affiliation_string":"Department of Mathematics Gandhigram Rural Institute-Deemed University, Gandhigram 624 302, Tamilnadu, India","institution_ids":["https://openalex.org/I880551032"]},{"raw_affiliation_string":"Department of Mathematics, Gandhigram Rural Institute ? Deemed University, Gandhigram-624 302, Tamilnadu, India","institution_ids":["https://openalex.org/I880551032"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038703355","display_name":"S. Lakshmanan","orcid":"https://orcid.org/0000-0002-4622-3782"},"institutions":[{"id":"https://openalex.org/I111575329","display_name":"Bharathiar University","ror":"https://ror.org/04fht8c22","country_code":"IN","type":"education","lineage":["https://openalex.org/I111575329"]},{"id":"https://openalex.org/I880551032","display_name":"Gandhigram Rural Institute","ror":"https://ror.org/01abtgj51","country_code":"IN","type":"education","lineage":["https://openalex.org/I880551032"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Shanmugam Lakshmanan","raw_affiliation_strings":["Department of Mathematics Bharathiar University, Coimbatore 641 046, Tamilnadu, India","Department of Mathematics Gandhigram Rural Institute-Deemed University, Gandhigram 624 302, Tamilnadu, India","Department of Mathematics, Gandhigram Rural Institute ? Deemed University, Gandhigram-624 302, Tamilnadu, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Bharathiar University, Coimbatore 641 046, Tamilnadu, India","institution_ids":["https://openalex.org/I111575329"]},{"raw_affiliation_string":"Department of Mathematics Gandhigram Rural Institute-Deemed University, Gandhigram 624 302, Tamilnadu, India","institution_ids":["https://openalex.org/I880551032"]},{"raw_affiliation_string":"Department of Mathematics, Gandhigram Rural Institute ? Deemed University, Gandhigram-624 302, Tamilnadu, India","institution_ids":["https://openalex.org/I880551032"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054227916","display_name":"R. Rakkiyappan","orcid":"https://orcid.org/0000-0003-0809-2782"},"institutions":[{"id":"https://openalex.org/I880551032","display_name":"Gandhigram Rural Institute","ror":"https://ror.org/01abtgj51","country_code":"IN","type":"education","lineage":["https://openalex.org/I880551032"]},{"id":"https://openalex.org/I111575329","display_name":"Bharathiar University","ror":"https://ror.org/04fht8c22","country_code":"IN","type":"education","lineage":["https://openalex.org/I111575329"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Rajan Rakkiyappan","raw_affiliation_strings":["Department of Mathematics Bharathiar University, Coimbatore 641 046, Tamilnadu, India","Department of Mathematics Gandhigram Rural Institute-Deemed University, Gandhigram 624 302, Tamilnadu, India","Department of Mathematics, Bharathiar University, Coimbatore\u00a0- 641 046, Tamilnadu, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Bharathiar University, Coimbatore 641 046, Tamilnadu, India","institution_ids":["https://openalex.org/I111575329"]},{"raw_affiliation_string":"Department of Mathematics Gandhigram Rural Institute-Deemed University, Gandhigram 624 302, Tamilnadu, India","institution_ids":["https://openalex.org/I880551032"]},{"raw_affiliation_string":"Department of Mathematics, Bharathiar University, Coimbatore\u00a0- 641 046, Tamilnadu, India","institution_ids":["https://openalex.org/I111575329"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015256521"],"corresponding_institution_ids":["https://openalex.org/I111575329","https://openalex.org/I880551032"],"apc_list":{"value":4080,"currency":"PLN","value_usd":1100},"apc_paid":{"value":4080,"currency":"PLN","value_usd":1100},"fwci":3.4091,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.91985673,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"22","issue":"2","first_page":"339","last_page":"351"},"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":0.9998999834060669,"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/T10046","display_name":"Stability and Control of Uncertain Systems","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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9894000291824341,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/mathematics","display_name":"Mathematics","score":0.7458841800689697},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.6658798456192017},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.550167441368103},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5436127185821533},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5262126922607422},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5101678371429443},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4351623058319092},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.42916956543922424},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4132364094257355},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3416014015674591},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21178880333900452},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.057468682527542114},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05045008659362793}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7458841800689697},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.6658798456192017},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.550167441368103},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5436127185821533},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5262126922607422},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5101678371429443},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4351623058319092},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.42916956543922424},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4132364094257355},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3416014015674591},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21178880333900452},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.057468682527542114},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05045008659362793},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2478/v10006-012-0025-6","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-012-0025-6","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-012-0025-6","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:10.1.1.390.6342","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.390.6342","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/amc2228.pdf","raw_type":"text"},{"id":"pmh:oai:figshare.com:article/20906692","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/LMI_optimization_problem_of_delay-dependent_robust_stability_criteria_for_stochastic_systems_with_polytopic_and_linear_fractional_uncertainties/20906692","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:zbc.uz.zgora.pl:46985","is_oa":false,"landing_page_url":"https://zbc.uz.zgora.pl/dlibra/docmetadata?showContent=true&id=46985","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=616","raw_type":"artyku\u0142"}],"best_oa_location":{"id":"doi:10.2478/v10006-012-0025-6","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-012-0025-6","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-012-0025-6","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/W1966164211.pdf","grobid_xml":"https://content.openalex.org/works/W1966164211.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W1506119886","https://openalex.org/W1575430033","https://openalex.org/W1575718442","https://openalex.org/W1599721123","https://openalex.org/W1607633954","https://openalex.org/W1880793639","https://openalex.org/W1991944848","https://openalex.org/W1994023414","https://openalex.org/W1996542094","https://openalex.org/W2004272198","https://openalex.org/W2005398461","https://openalex.org/W2005489760","https://openalex.org/W2012527250","https://openalex.org/W2021510361","https://openalex.org/W2022706157","https://openalex.org/W2035833389","https://openalex.org/W2040376305","https://openalex.org/W2049381481","https://openalex.org/W2052756958","https://openalex.org/W2055467990","https://openalex.org/W2061951967","https://openalex.org/W2062160141","https://openalex.org/W2062805416","https://openalex.org/W2065740685","https://openalex.org/W2076368645","https://openalex.org/W2082256594","https://openalex.org/W2085481535","https://openalex.org/W2087080682","https://openalex.org/W2106227572","https://openalex.org/W2109310060","https://openalex.org/W2111934871","https://openalex.org/W2116644917","https://openalex.org/W2117216822","https://openalex.org/W2144737232","https://openalex.org/W2144788107","https://openalex.org/W2153027817","https://openalex.org/W2156573928","https://openalex.org/W2170354024","https://openalex.org/W2171539754","https://openalex.org/W2404414373","https://openalex.org/W3142427345","https://openalex.org/W3210839039","https://openalex.org/W4211202937"],"related_works":["https://openalex.org/W3013085049","https://openalex.org/W1560496689","https://openalex.org/W4386900933","https://openalex.org/W4385301946","https://openalex.org/W4297797135","https://openalex.org/W3125672081","https://openalex.org/W1673581201","https://openalex.org/W2991991550","https://openalex.org/W64182352","https://openalex.org/W4289799755"],"abstract_inverted_index":{"LMI":[0,21],"optimization":[1,22],"problem":[2,23],"of":[3,24,58,97,105,124],"delay-dependent":[4,25,90],"robust":[5,26],"stability":[6,27,88,91],"criteria":[7,28,92],"for":[8,29],"stochastic":[9,30,87],"systems":[10,31],"with":[11,32],"polytopic":[12,33],"and":[13,34,45,55,72,86,128],"linear":[14,35,73],"fractional":[15,36,74],"uncertainties":[16],"This":[17],"paper":[18],"studies":[19],"an":[20,131],"uncertainties.":[37],"The":[38,65],"delay":[39,62],"is":[40,108],"assumed":[41],"to":[42,47,110,120,129],"be":[43],"time-varying":[44,61],"belong":[46],"a":[48],"given":[49,119],"interval,":[50],"which":[51],"means":[52],"that":[53],"lower":[54],"upper":[56],"bounds":[57],"this":[59],"interval":[60],"are":[63,93,118],"available.":[64],"uncertainty":[66,71],"under":[67],"consideration":[68],"includes":[69],"polytopic-type":[70],"norm-bounded":[75],"uncertainty.":[76],"Based":[77],"on":[78],"the":[79,103,122,125,138],"new":[80],"Lyapunov-Krasovskii":[81],"functional,":[82],"some":[83,134],"inequality":[84],"techniques":[85],"theory,":[89],"obtained":[94],"in":[95,137],"terms":[96],"Linear":[98],"Matrix":[99],"Inequalities":[100],"(LMIs).":[101],"Moreover,":[102],"derivative":[104],"time":[106],"delays":[107],"allowed":[109],"take":[111],"any":[112],"value.":[113],"Finally,":[114],"four":[115],"numerical":[116],"examples":[117],"illustrate":[121],"effectiveness":[123],"proposed":[126],"method":[127],"show":[130],"improvement":[132],"over":[133],"results":[135],"found":[136],"literature.":[139]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}