{"id":"https://openalex.org/W2525312619","doi":"https://doi.org/10.1109/tnnls.2016.2608879","title":"Delay-Dependent Global Exponential Stability for Delayed Recurrent Neural Networks","display_name":"Delay-Dependent Global Exponential Stability for Delayed Recurrent Neural Networks","publication_year":2016,"publication_date":"2016-09-29","ids":{"openalex":"https://openalex.org/W2525312619","doi":"https://doi.org/10.1109/tnnls.2016.2608879","mag":"2525312619","pmid":"https://pubmed.ncbi.nlm.nih.gov/27705864"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2016.2608879","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2016.2608879","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5088234880","display_name":"Yin Sheng","orcid":"https://orcid.org/0000-0003-4698-5100"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yin Sheng","raw_affiliation_strings":["Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, School of Automation, Huazhong University of Science and Technology, Wuhan, China"],"raw_orcid":"https://orcid.org/0000-0003-4698-5100","affiliations":[{"raw_affiliation_string":"Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, School of Automation, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yi Shen","orcid":"https://orcid.org/0000-0002-0663-3365"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yi Shen","raw_affiliation_strings":["Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, School of Automation, Huazhong University of Science and Technology, Wuhan, China"],"raw_orcid":"https://orcid.org/0000-0002-0663-3365","affiliations":[{"raw_affiliation_string":"Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, School of Automation, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108545008","display_name":"Mingfu Zhu","orcid":null},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mingfu Zhu","raw_affiliation_strings":["Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, School of Automation, Huazhong University of Science and Technology, Wuhan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, School of Automation, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I47720641"],"apc_list":null,"apc_paid":null,"fwci":7.6946,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.97302055,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"28","issue":"12","first_page":"2974","last_page":"2984"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":1.0,"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/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.991599977016449,"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/exponential-stability","display_name":"Exponential stability","score":0.8691389560699463},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.7902448177337646},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6660126447677612},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5562324523925781},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5447067618370056},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5237448215484619},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4749722182750702},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.417818158864975},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4159083664417267},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3909049332141876},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.35352998971939087},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.2561875879764557},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2309553325176239},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15050193667411804},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.0727059543132782},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06617903709411621},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.0492837131023407},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.046988993883132935}],"concepts":[{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.8691389560699463},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.7902448177337646},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6660126447677612},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5562324523925781},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5447067618370056},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5237448215484619},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4749722182750702},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.417818158864975},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4159083664417267},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3909049332141876},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.35352998971939087},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.2561875879764557},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2309553325176239},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15050193667411804},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0727059543132782},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06617903709411621},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0492837131023407},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.046988993883132935},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"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/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2016.2608879","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2016.2608879","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:27705864","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/27705864","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3035389536","display_name":null,"funder_award_id":"61374150","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G638264298","display_name":null,"funder_award_id":"2015BHE013","funder_id":"https://openalex.org/F4320334974","funder_display_name":"Hebei Province Science and Technology Support Program"},{"id":"https://openalex.org/G6431221768","display_name":null,"funder_award_id":"61134012","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6828728677","display_name":null,"funder_award_id":"11271146","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334974","display_name":"Hebei Province Science and Technology Support Program","ror":"https://ror.org/05a7g7f24"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W565987384","https://openalex.org/W1494628843","https://openalex.org/W1922858971","https://openalex.org/W1931775713","https://openalex.org/W1962309857","https://openalex.org/W1971186708","https://openalex.org/W1972665816","https://openalex.org/W1973352490","https://openalex.org/W1974044289","https://openalex.org/W1993920342","https://openalex.org/W1995539259","https://openalex.org/W1999362577","https://openalex.org/W2003403621","https://openalex.org/W2016562720","https://openalex.org/W2025249731","https://openalex.org/W2031673504","https://openalex.org/W2034707592","https://openalex.org/W2037686415","https://openalex.org/W2038641684","https://openalex.org/W2039375846","https://openalex.org/W2044467507","https://openalex.org/W2048584165","https://openalex.org/W2048646957","https://openalex.org/W2049386744","https://openalex.org/W2051104796","https://openalex.org/W2056717940","https://openalex.org/W2062564145","https://openalex.org/W2079871064","https://openalex.org/W2082778383","https://openalex.org/W2095515103","https://openalex.org/W2097208820","https://openalex.org/W2101879828","https://openalex.org/W2105443770","https://openalex.org/W2107194000","https://openalex.org/W2110460555","https://openalex.org/W2111906242","https://openalex.org/W2117976551","https://openalex.org/W2120272661","https://openalex.org/W2121615270","https://openalex.org/W2123268478","https://openalex.org/W2125107639","https://openalex.org/W2126341830","https://openalex.org/W2132552866","https://openalex.org/W2145903916","https://openalex.org/W2145963278","https://openalex.org/W2146569872","https://openalex.org/W2150344394","https://openalex.org/W2152361984","https://openalex.org/W2160361732","https://openalex.org/W2161534096","https://openalex.org/W2164537164","https://openalex.org/W2169539509","https://openalex.org/W2170001575","https://openalex.org/W2284760372","https://openalex.org/W2403865117","https://openalex.org/W4211124809"],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1097487277","https://openalex.org/W2949964783","https://openalex.org/W2768610039","https://openalex.org/W3121250382","https://openalex.org/W4285390085","https://openalex.org/W31688704","https://openalex.org/W1883388834","https://openalex.org/W2941078816","https://openalex.org/W940406003"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3],"the":[4,22,63,103,108],"global":[5,32,51,74,88],"exponential":[6,33,52,64,89],"stability":[7,34,53,76,90],"for":[8,55],"delayed":[9],"recurrent":[10],"neural":[11],"networks":[12],"(DRNNs).":[13],"By":[14],"constructing":[15],"an":[16],"augmented":[17],"Lyapunov-Krasovskii":[18],"functional":[19],"and":[20,27,47,105],"adopting":[21],"reciprocally":[23],"convex":[24],"combination":[25],"approach":[26],"Wirtinger-based":[28],"integral":[29],"inequality,":[30],"delay-dependent":[31],"criteria":[35,77],"are":[36],"derived":[37],"in":[38,81],"terms":[39],"of":[40,78,107],"linear":[41],"matrix":[42],"inequalities.":[43],"Meanwhile,":[44],"a":[45,60,93],"general":[46],"effective":[48],"method":[49],"on":[50],"analysis":[54],"DRNNs":[56,79],"is":[57,98],"given":[58],"through":[59],"lemma,":[61,72],"where":[62],"convergence":[65],"rate":[66],"can":[67,84],"be":[68,85],"estimated.":[69],"With":[70],"this":[71],"some":[73],"asymptotic":[75],"acquired":[80],"previous":[82],"studies":[83],"generalized":[86],"to":[87,101],"ones.":[91],"Finally,":[92],"frequently":[94],"utilized":[95],"numerical":[96],"example":[97],"carried":[99],"out":[100],"illustrate":[102],"effectiveness":[104],"merits":[106],"proposed":[109],"theoretical":[110],"results.":[111]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-21T08:15:58.654021","created_date":"2025-10-10T00:00:00"}