{"id":"https://openalex.org/W2804783771","doi":"https://doi.org/10.1109/tnnls.2018.2830789","title":"Exponential Stability Analysis for Delayed Semi-Markovian Recurrent Neural Networks: A Homogeneous Polynomial Approach","display_name":"Exponential Stability Analysis for Delayed Semi-Markovian Recurrent Neural Networks: A Homogeneous Polynomial Approach","publication_year":2018,"publication_date":"2018-05-18","ids":{"openalex":"https://openalex.org/W2804783771","doi":"https://doi.org/10.1109/tnnls.2018.2830789","mag":"2804783771","pmid":"https://pubmed.ncbi.nlm.nih.gov/29994551"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2018.2830789","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2018.2830789","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/A5100353964","display_name":"Xin Li","orcid":"https://orcid.org/0000-0002-8771-2478"},"institutions":[{"id":"https://openalex.org/I55022517","display_name":"Heilongjiang University","ror":"https://ror.org/04zyhq975","country_code":"CN","type":"education","lineage":["https://openalex.org/I55022517"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xin Li","raw_affiliation_strings":["School of Mathematical Science, Heilongjiang University, Harbin, China"],"raw_orcid":"https://orcid.org/0000-0002-8771-2478","affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Heilongjiang University, Harbin, China","institution_ids":["https://openalex.org/I55022517"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035583615","display_name":"Fanbiao Li","orcid":"https://orcid.org/0000-0002-4237-855X"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fanbiao Li","raw_affiliation_strings":["School of Information Science and Engineering, Central South University, Changsha, China"],"raw_orcid":"https://orcid.org/0000-0002-4237-855X","affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101841009","display_name":"Xian Zhang","orcid":"https://orcid.org/0000-0001-7023-7351"},"institutions":[{"id":"https://openalex.org/I55022517","display_name":"Heilongjiang University","ror":"https://ror.org/04zyhq975","country_code":"CN","type":"education","lineage":["https://openalex.org/I55022517"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xian Zhang","raw_affiliation_strings":["School of Mathematical Science, Heilongjiang University, Harbin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Heilongjiang University, Harbin, China","institution_ids":["https://openalex.org/I55022517"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108047088","display_name":"Chunhua Yang","orcid":"https://orcid.org/0000-0003-2550-1509"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chunhua Yang","raw_affiliation_strings":["School of Information Science and Engineering, Central South University, Changsha, China"],"raw_orcid":"https://orcid.org/0000-0003-2550-1509","affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100711522","display_name":"Weihua Gui","orcid":"https://orcid.org/0000-0003-0312-436X"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weihua Gui","raw_affiliation_strings":["School of Information Science and Engineering, Central South University, Changsha, China"],"raw_orcid":"https://orcid.org/0000-0003-0312-436X","affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Central South University, Changsha, China","institution_ids":["https://openalex.org/I139660479"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":11.1833,"has_fulltext":false,"cited_by_count":101,"citation_normalized_percentile":{"value":0.98601043,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"29","issue":"12","first_page":"6374","last_page":"6384"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9998999834060669,"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":0.9998999834060669,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9944999814033508,"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":0.607215404510498},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5869397521018982},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5866086483001709},{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.5583940148353577},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5319965481758118},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.5112500190734863},{"id":"https://openalex.org/keywords/homogeneous-polynomial","display_name":"Homogeneous polynomial","score":0.4844805896282196},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4784236550331116},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4688127040863037},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.450398325920105},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.34417733550071716},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3376186490058899},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.23084288835525513},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15585067868232727},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12034174799919128},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08396780490875244},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07906299829483032},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07049021124839783}],"concepts":[{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.607215404510498},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5869397521018982},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5866086483001709},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.5583940148353577},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5319965481758118},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5112500190734863},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.4844805896282196},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4784236550331116},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4688127040863037},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.450398325920105},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.34417733550071716},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3376186490058899},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.23084288835525513},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15585067868232727},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12034174799919128},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08396780490875244},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07906299829483032},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07049021124839783},{"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"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/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/tnnls.2018.2830789","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2018.2830789","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:29994551","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/29994551","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/G2158780659","display_name":null,"funder_award_id":"2017CX005","funder_id":"https://openalex.org/F4320321514","funder_display_name":"Central South University"},{"id":"https://openalex.org/G5442932911","display_name":null,"funder_award_id":"61321003","funder_id":"https://openalex.org/F4320327720","funder_display_name":"Foundation for Innovative Research Groups of the National Natural Science Foundation of China"},{"id":"https://openalex.org/G5559763919","display_name":null,"funder_award_id":"61603417","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8305113123","display_name":null,"funder_award_id":"11371006","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/F4320321514","display_name":"Central South University","ror":"https://ror.org/00f1zfq44"},{"id":"https://openalex.org/F4320327720","display_name":"Foundation for Innovative Research Groups of the National Natural Science Foundation of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W200796656","https://openalex.org/W1030937500","https://openalex.org/W1500568346","https://openalex.org/W1645305843","https://openalex.org/W1967965856","https://openalex.org/W1970491161","https://openalex.org/W1976576497","https://openalex.org/W1984797175","https://openalex.org/W1991462851","https://openalex.org/W1992635849","https://openalex.org/W2007894359","https://openalex.org/W2007952299","https://openalex.org/W2012752557","https://openalex.org/W2037644696","https://openalex.org/W2043241145","https://openalex.org/W2048942281","https://openalex.org/W2064770819","https://openalex.org/W2067168419","https://openalex.org/W2075671688","https://openalex.org/W2115370288","https://openalex.org/W2132552866","https://openalex.org/W2132917374","https://openalex.org/W2137077153","https://openalex.org/W2159468916","https://openalex.org/W2161354519","https://openalex.org/W2168074109","https://openalex.org/W2242049308","https://openalex.org/W2331514810","https://openalex.org/W2331916262","https://openalex.org/W2342488082","https://openalex.org/W2379133119","https://openalex.org/W2510108600","https://openalex.org/W2515927598","https://openalex.org/W2605110917","https://openalex.org/W2623080715","https://openalex.org/W7045592886"],"related_works":["https://openalex.org/W2951408545","https://openalex.org/W2327776733","https://openalex.org/W4313854677","https://openalex.org/W2315521207","https://openalex.org/W2741030450","https://openalex.org/W2263629155","https://openalex.org/W4300091438","https://openalex.org/W1508761541","https://openalex.org/W1997200860","https://openalex.org/W1995529814"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"the":[3,37,47,58,63,72,103,106],"exponential":[4,38],"stability":[5,41,73],"analysis":[6],"issue":[7],"for":[8,46,62,84],"a":[9,22,87],"class":[10],"of":[11,90,105],"delayed":[12,64],"recurrent":[13],"neural":[14,49],"networks":[15,50],"(RNNs)":[16],"with":[17,51,67,86],"semi-Markovian":[18],"parameters.":[19],"By":[20],"constructing":[21],"stochastic":[23],"Lyapunov":[24],"functional":[25],"and":[26],"using":[27],"some":[28],"zoom":[29],"techniques":[30],"to":[31,101],"estimate":[32],"its":[33],"weak":[34],"infinitesimal":[35],"operator,":[36],"mean":[39],"square":[40],"criteria":[42],"have":[43,77],"been":[44],"proposed":[45,107],"Markovian":[48,65],"certain":[52],"transition":[53,69],"probabilities.":[54],"We":[55],"then":[56],"generalize":[57],"homogeneous":[59,92],"polynomial":[60,93],"approach":[61],"RNNs":[66],"uncertain":[68],"probabilities":[70],"during":[71],"analysis.":[74],"Theoretical":[75],"results":[76],"obtained":[78],"by":[79],"introducing":[80],"an":[81],"appropriate":[82],"technique":[83],"dealing":[85],"large":[88],"number":[89],"complex":[91],"matrix":[94],"inequalities.":[95],"Finally,":[96],"numerical":[97],"examples":[98],"are":[99],"provided":[100],"demonstrate":[102],"effectiveness":[104],"technique.":[108]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":19},{"year":2019,"cited_by_count":21},{"year":2018,"cited_by_count":5}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}