{"id":"https://openalex.org/W3094536093","doi":"https://doi.org/10.1109/tcyb.2020.3025754","title":"Novel Fixed-Time Stability Criteria for Discontinuous Nonautonomous Systems: Lyapunov Method With Indefinite Derivative","display_name":"Novel Fixed-Time Stability Criteria for Discontinuous Nonautonomous Systems: Lyapunov Method With Indefinite Derivative","publication_year":2020,"publication_date":"2020-10-21","ids":{"openalex":"https://openalex.org/W3094536093","doi":"https://doi.org/10.1109/tcyb.2020.3025754","mag":"3094536093","pmid":"https://pubmed.ncbi.nlm.nih.gov/33085627"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2020.3025754","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2020.3025754","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/A5089530658","display_name":"Zuowei Cai","orcid":"https://orcid.org/0000-0003-4470-7107"},"institutions":[{"id":"https://openalex.org/I87318903","display_name":"Hunan Women'S University","ror":"https://ror.org/032bw1116","country_code":"CN","type":"education","lineage":["https://openalex.org/I87318903"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zuowei Cai","raw_affiliation_strings":["School of Information Science and Engineering, Hunan Women’s University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Hunan Women’s University, Changsha, China","institution_ids":["https://openalex.org/I87318903"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101910473","display_name":"Lihong Huang","orcid":"https://orcid.org/0000-0001-8691-5532"},"institutions":[{"id":"https://openalex.org/I56934997","display_name":"Changsha University of Science and Technology","ror":"https://ror.org/03yph8055","country_code":"CN","type":"education","lineage":["https://openalex.org/I56934997"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lihong Huang","raw_affiliation_strings":["School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, China","institution_ids":["https://openalex.org/I56934997"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058450211","display_name":"Zengyun Wang","orcid":"https://orcid.org/0000-0002-2046-4078"},"institutions":[{"id":"https://openalex.org/I916048824","display_name":"Hunan First Normal University","ror":"https://ror.org/00s9d1a36","country_code":"CN","type":"education","lineage":["https://openalex.org/I916048824"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zengyun Wang","raw_affiliation_strings":["School of Mathematics and Computational Science, Hunan First Normal University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Hunan First Normal University, Changsha, China","institution_ids":["https://openalex.org/I916048824"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089530658"],"corresponding_institution_ids":["https://openalex.org/I87318903"],"apc_list":null,"apc_paid":null,"fwci":5.4179,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.96383301,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"52","issue":"6","first_page":"4286","last_page":"4299"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"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":0.9965999722480774,"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/T10244","display_name":"Chaos control and synchronization","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.8193371295928955},{"id":"https://openalex.org/keywords/differential-inclusion","display_name":"Differential inclusion","score":0.7631984353065491},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7283682823181152},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.6906375288963318},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5279666185379028},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.49142491817474365},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.46216392517089844},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4621250331401825},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43440061807632446},{"id":"https://openalex.org/keywords/almost-everywhere","display_name":"Almost everywhere","score":0.429298996925354},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3593410849571228},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.30547332763671875},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.15183022618293762},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.13745352625846863},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1301470696926117}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.8193371295928955},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.7631984353065491},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7283682823181152},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6906375288963318},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5279666185379028},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.49142491817474365},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.46216392517089844},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4621250331401825},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43440061807632446},{"id":"https://openalex.org/C27142425","wikidata":"https://www.wikidata.org/wiki/Q1139334","display_name":"Almost everywhere","level":2,"score":0.429298996925354},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3593410849571228},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.30547332763671875},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.15183022618293762},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.13745352625846863},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1301470696926117},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1109/tcyb.2020.3025754","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2020.3025754","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:33085627","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33085627","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":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.8100000023841858}],"awards":[{"id":"https://openalex.org/G8041828821","display_name":null,"funder_award_id":"11701172","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W223797242","https://openalex.org/W1484590079","https://openalex.org/W1551360398","https://openalex.org/W1960239420","https://openalex.org/W1964328481","https://openalex.org/W1986453347","https://openalex.org/W1988837728","https://openalex.org/W1996054106","https://openalex.org/W2010709227","https://openalex.org/W2011100809","https://openalex.org/W2015113370","https://openalex.org/W2016315140","https://openalex.org/W2017333682","https://openalex.org/W2019499606","https://openalex.org/W2040174802","https://openalex.org/W2048723778","https://openalex.org/W2049589722","https://openalex.org/W2052883072","https://openalex.org/W2056537430","https://openalex.org/W2060446060","https://openalex.org/W2075702421","https://openalex.org/W2083670272","https://openalex.org/W2091608925","https://openalex.org/W2121221397","https://openalex.org/W2121385949","https://openalex.org/W2125292024","https://openalex.org/W2132723283","https://openalex.org/W2138393638","https://openalex.org/W2146141645","https://openalex.org/W2150325136","https://openalex.org/W2195244501","https://openalex.org/W2327720711","https://openalex.org/W2345071365","https://openalex.org/W2416581454","https://openalex.org/W2491461032","https://openalex.org/W2564808818","https://openalex.org/W2586402706","https://openalex.org/W2587797689","https://openalex.org/W2735981021","https://openalex.org/W2754524650","https://openalex.org/W2782819892","https://openalex.org/W2789369557","https://openalex.org/W2797063385","https://openalex.org/W2800188922","https://openalex.org/W2811259241","https://openalex.org/W2889379237","https://openalex.org/W2904213097","https://openalex.org/W2907691972","https://openalex.org/W2913621502","https://openalex.org/W2946330977","https://openalex.org/W2962871882","https://openalex.org/W2965717425","https://openalex.org/W3101307053","https://openalex.org/W4210718478","https://openalex.org/W4251507077","https://openalex.org/W4293078920","https://openalex.org/W6682468742"],"related_works":["https://openalex.org/W2371448224","https://openalex.org/W3134495997","https://openalex.org/W2363680170","https://openalex.org/W2061781961","https://openalex.org/W2376428685","https://openalex.org/W4256082577","https://openalex.org/W625783435","https://openalex.org/W1971476769","https://openalex.org/W3031270005","https://openalex.org/W3137838997"],"abstract_inverted_index":{"This":[0],"article":[1,60],"considers":[2],"a":[3,95],"general":[4],"class":[5],"of":[6,23,30,41,58,75,109,126,140,148],"nonautonomous":[7],"discontinuous":[8,24],"ordinary":[9],"differential":[10,31],"equations":[11],"(ODE).":[12],"By":[13],"constructing":[14],"the":[15,18,38,42,47,72,76,79,106,114,121,146],"Filippov":[16],"multimap,":[17],"fixed-time":[19,122],"stability":[20],"(FTS)":[21],"problem":[22],"ODE":[25],"is":[26,53,61,82,111,142],"transformed":[27],"into":[28],"that":[29],"inclusion":[32],"(DI).":[33],"In":[34],"order":[35],"to":[36,63,84,119],"establish":[37],"FTS":[39,102,110,141],"criteria":[40],"zero":[43],"solution":[44],"for":[45,68,92,101],"DI,":[46],"generalized":[48,56],"Lyapunov":[49],"function":[50],"(LF)":[51],"method":[52,139],"developed.":[54],"The":[55,136],"LF":[57,81,138],"this":[59],"relaxed":[62],"have":[64],"an":[65],"indefinite":[66],"derivative":[67,91],"almost":[69],"everywhere":[70],"along":[71],"state":[73],"trajectories":[74],"system.":[77],"However,":[78],"traditional":[80],"required":[83],"possess":[85],"negative":[86],"definite":[87,90],"or":[88],"semi-negative":[89],"everywhere.":[93],"As":[94],"result,":[96],"several":[97],"novel":[98],"sufficient":[99],"conditions":[100],"are":[103,117],"given.":[104],"Moreover,":[105],"settling":[107],"time":[108],"provided.":[112],"Then,":[113],"theoretical":[115],"results":[116],"applied":[118],"solve":[120],"stabilization":[123],"control":[124,149],"problems":[125],"ball":[127],"motion":[128],"model":[129],"and":[130],"neural":[131],"networks":[132],"(NNs)":[133],"with":[134],"discontinuities.":[135],"developed":[137],"extremely":[143],"significant":[144],"in":[145],"field":[147],"engineering.":[150]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}