{"id":"https://openalex.org/W2963700934","doi":"https://doi.org/10.1109/tcyb.2019.2926537","title":"Robust Stability of Recurrent Neural Networks With Time-Varying Delays and Input Perturbation","display_name":"Robust Stability of Recurrent Neural Networks With Time-Varying Delays and Input Perturbation","publication_year":2019,"publication_date":"2019-07-22","ids":{"openalex":"https://openalex.org/W2963700934","doi":"https://doi.org/10.1109/tcyb.2019.2926537","mag":"2963700934","pmid":"https://pubmed.ncbi.nlm.nih.gov/31329152"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2019.2926537","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2019.2926537","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","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/A5041604044","display_name":"Fanghai Zhang","orcid":"https://orcid.org/0000-0002-6022-7499"},"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":true,"raw_author_name":"Fanghai Zhang","raw_affiliation_strings":["School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, China","School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081245089","display_name":"Zhigang Zeng","orcid":"https://orcid.org/0000-0003-4587-3588"},"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":"Zhigang Zeng","raw_affiliation_strings":["Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Huazhong University of Science and Technology, Wuhan, China","School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I47720641"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5041604044"],"corresponding_institution_ids":["https://openalex.org/I47720641"],"apc_list":null,"apc_paid":null,"fwci":1.6711,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.85685442,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"51","issue":"6","first_page":"3027","last_page":"3038"},"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":0.9930999875068665,"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/T10608","display_name":"Neurogenesis and neuroplasticity mechanisms","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/2806","display_name":"Developmental Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.7667237520217896},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.7358707785606384},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5689923763275146},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5501959919929504},{"id":"https://openalex.org/keywords/content-addressable-memory","display_name":"Content-addressable memory","score":0.5456550121307373},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4792913794517517},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.4599562883377075},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.43486952781677246},{"id":"https://openalex.org/keywords/multistability","display_name":"Multistability","score":0.42392563819885254},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.42118144035339355},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37021052837371826},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3204575777053833},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2347283959388733},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07715633511543274}],"concepts":[{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.7667237520217896},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.7358707785606384},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5689923763275146},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5501959919929504},{"id":"https://openalex.org/C53442348","wikidata":"https://www.wikidata.org/wiki/Q745101","display_name":"Content-addressable memory","level":3,"score":0.5456550121307373},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4792913794517517},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4599562883377075},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.43486952781677246},{"id":"https://openalex.org/C2776966350","wikidata":"https://www.wikidata.org/wiki/Q6935096","display_name":"Multistability","level":3,"score":0.42392563819885254},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.42118144035339355},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37021052837371826},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3204575777053833},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2347283959388733},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07715633511543274},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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":2,"locations":[{"id":"doi:10.1109/tcyb.2019.2926537","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2019.2926537","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Cybernetics","raw_type":"journal-article"},{"id":"pmid:31329152","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/31329152","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 cybernetics","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2413230818","display_name":null,"funder_award_id":"61821003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G282535699","display_name":null,"funder_award_id":"2017CFA005","funder_id":"https://openalex.org/F4320327654","funder_display_name":"Foundation for Innovative Research Groups of Hubei Province of China"},{"id":"https://openalex.org/G3476586388","display_name":null,"funder_award_id":"61673188","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4222534746","display_name":null,"funder_award_id":"2016YFB0800402","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G7099877325","display_name":null,"funder_award_id":"61761130081","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/F4320327654","display_name":"Foundation for Innovative Research Groups of Hubei Province of China","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W1967374767","https://openalex.org/W1978048454","https://openalex.org/W1980475044","https://openalex.org/W1998253129","https://openalex.org/W2014116791","https://openalex.org/W2016315140","https://openalex.org/W2039375846","https://openalex.org/W2045445942","https://openalex.org/W2056717940","https://openalex.org/W2059162909","https://openalex.org/W2062210787","https://openalex.org/W2065134213","https://openalex.org/W2072434871","https://openalex.org/W2073030819","https://openalex.org/W2074474916","https://openalex.org/W2112264578","https://openalex.org/W2117288934","https://openalex.org/W2121752938","https://openalex.org/W2121973871","https://openalex.org/W2148418614","https://openalex.org/W2150534501","https://openalex.org/W2164344254","https://openalex.org/W2167320656","https://openalex.org/W2287065438","https://openalex.org/W2306429512","https://openalex.org/W2337918798","https://openalex.org/W2343487611","https://openalex.org/W2400440531","https://openalex.org/W2400963224","https://openalex.org/W2416581454","https://openalex.org/W2501582773","https://openalex.org/W2505702157","https://openalex.org/W2520103018","https://openalex.org/W2554850913","https://openalex.org/W2582971624","https://openalex.org/W2587243229","https://openalex.org/W2590369426","https://openalex.org/W2605925875","https://openalex.org/W2625250219","https://openalex.org/W2733258593","https://openalex.org/W2762057394","https://openalex.org/W2768517680","https://openalex.org/W2776574981","https://openalex.org/W2793208116","https://openalex.org/W2793274122","https://openalex.org/W2850531805","https://openalex.org/W2899582485","https://openalex.org/W2962807165","https://openalex.org/W3152129208","https://openalex.org/W4285719527","https://openalex.org/W6740742641","https://openalex.org/W6793799482"],"related_works":["https://openalex.org/W4226329279","https://openalex.org/W1527571384","https://openalex.org/W2383189914","https://openalex.org/W4301445084","https://openalex.org/W2963840034","https://openalex.org/W1984975294","https://openalex.org/W4226178663","https://openalex.org/W1517717759","https://openalex.org/W3198721837","https://openalex.org/W2057553352"],"abstract_inverted_index":{"This":[0],"paper":[1,136],"addresses":[2],"the":[3,18,28,40,51,60,79,94,99,118,128,140,147,154,157],"robust":[4,41,52],"stability":[5,42,119,142],"of":[6,43,54,81,120,156],"recurrent":[7],"neural":[8,55,121],"networks":[9,56,122],"(RNNs)":[10],"with":[11,45,127],"time-varying":[12,19],"delays":[13,20],"and":[14,23,47,64,78,96,104,123,138],"input":[15,62,76,90,124],"perturbation,":[16,77],"where":[17],"include":[21],"discrete":[22,46],"distributed":[24,48],"delays.":[25,49],"By":[26],"employing":[27],"new":[29],"\u03c8":[30],"-type":[31],"integral":[32],"inequality,":[33],"several":[34],"sufficient":[35],"conditions":[36,132],"are":[37,150],"derived":[38],"for":[39,85],"RNNs":[44,69,82],"Meanwhile,":[50],"boundedness":[53],"is":[57,83,110,114],"explored":[58],"by":[59],"bounded":[61],"perturbation":[63,91],"L<sup>1</sup>":[65],"-norm":[66],"constraint.":[67],"Moreover,":[68],"have":[70],"a":[71,115],"strong":[72],"anti-jamming":[73],"ability":[74],"to":[75,93,152],"robustness":[80],"suitable":[84],"associative":[86],"memory.":[87],"Specifically,":[88],"when":[89],"belongs":[92],"specified":[95],"well-characterized":[97],"space,":[98],"results":[100],"cover":[101],"both":[102],"monostability":[103],"multistability":[105],"as":[106],"special":[107],"cases.":[108],"It":[109],"revealed":[111],"that":[112],"there":[113],"relationship":[116],"between":[117],"perturbation.":[125],"Compared":[126],"existing":[129,141],"results,":[130],"these":[131],"proposed":[133],"in":[134,143],"this":[135],"improve":[137],"extend":[139],"some":[144],"literature.":[145],"Finally,":[146],"numerical":[148],"examples":[149],"given":[151],"substantiate":[153],"effectiveness":[155],"theoretical":[158],"results.":[159]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}