{"id":"https://openalex.org/W1995309583","doi":"https://doi.org/10.1134/s0081543810050159","title":"Extension of E.A. Barbashin\u2019s and N.N. Krasovskii\u2019s stability theorems to controlled dynamical systems","display_name":"Extension of E.A. Barbashin\u2019s and N.N. Krasovskii\u2019s stability theorems to controlled dynamical systems","publication_year":2010,"publication_date":"2010-04-01","ids":{"openalex":"https://openalex.org/W1995309583","doi":"https://doi.org/10.1134/s0081543810050159","mag":"1995309583"},"language":"en","primary_location":{"id":"doi:10.1134/s0081543810050159","doi":"https://doi.org/10.1134/s0081543810050159","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0081543810050159","pdf_url":null,"source":{"id":"https://openalex.org/S4210176787","display_name":"Proceedings of the Steklov Institute of Mathematics","issn_l":"0081-5438","issn":["0081-5438","1531-8605"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Steklov Institute of Mathematics","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W1995309583"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref"],"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/A5077445872","display_name":"Elena Aleksandrovna Panasenko","orcid":"https://orcid.org/0000-0002-4737-9906","observed_orcids":["https://orcid.org/0000-0002-4737-9906"]},"institutions":[{"id":"https://openalex.org/I108321963","display_name":"Tambov State University","ror":"https://ror.org/05fzc8c45","country_code":"RU","type":"education","lineage":["https://openalex.org/I108321963"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"E. A. Panasenko","raw_affiliation_strings":["Tambov State University, ul. Internatsional\u2019naya 33, Tambov, 392000, Russia","Tambov State Univ"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tambov State University, ul. Internatsional\u2019naya 33, Tambov, 392000, Russia","institution_ids":["https://openalex.org/I108321963"]},{"raw_affiliation_string":"Tambov State Univ","institution_ids":["https://openalex.org/I108321963"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019984907","display_name":"E. L. Tonkov","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I57570584","display_name":"Udmurt State University","ror":"https://ror.org/00yp6m473","country_code":"RU","type":"education","lineage":["https://openalex.org/I57570584"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"E. L. Tonkov","raw_affiliation_strings":["Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russia","Udmurt state university"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russia","institution_ids":["https://openalex.org/I57570584"]},{"raw_affiliation_string":"Udmurt state university","institution_ids":["https://openalex.org/I57570584"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5077445872"],"corresponding_institution_ids":["https://openalex.org/I108321963"],"apc_list":null,"apc_paid":null,"fwci":1.3039,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.74587046,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"268","issue":"S1","first_page":"204","last_page":"221"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.7480000257492065,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.7480000257492065,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.0869000032544136,"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":0.06379999965429306,"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/asymptotic-stability","display_name":"asymptotic stability","score":0.8889999985694885},{"id":"https://openalex.org/keywords/global-stability","display_name":"global stability","score":0.9900000095367432},{"id":"https://openalex.org/keywords/stability-of-equilibrium","display_name":"equilibrium stability","score":0.7919999957084656},{"id":"https://openalex.org/keywords/controlled-dynamical-systems","display_name":"controlled dynamical systems","score":0.9779999852180481}],"concepts":[{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.9275254011154175},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7931159734725952},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6143277883529663},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6002091765403748},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5850170850753784},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5405425429344177},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.5378808975219727},{"id":"https://openalex.org/C141898687","wikidata":"https://www.wikidata.org/wiki/Q1501997","display_name":"Hausdorff distance","level":2,"score":0.5144010186195374},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5038701891899109},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.49412181973457336},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4408305585384369},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.4273323118686676},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.41016435623168945},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39605677127838135},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.13715630769729614},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.09220930933952332},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07711911201477051},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06938591599464417},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s0081543810050159","doi":"https://doi.org/10.1134/s0081543810050159","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0081543810050159","pdf_url":null,"source":{"id":"https://openalex.org/S4210176787","display_name":"Proceedings of the Steklov Institute of Mathematics","issn_l":"0081-5438","issn":["0081-5438","1531-8605"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Steklov Institute of Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1546156674","https://openalex.org/W1551360398","https://openalex.org/W1592648094","https://openalex.org/W1966397236","https://openalex.org/W2030148719","https://openalex.org/W2030978552","https://openalex.org/W2035518322","https://openalex.org/W2112415766","https://openalex.org/W2597868418","https://openalex.org/W3021722416","https://openalex.org/W4254649238","https://openalex.org/W4293078920"],"related_works":["https://openalex.org/W2049790054","https://openalex.org/W49331310","https://openalex.org/W49793852","https://openalex.org/W3179356943","https://openalex.org/W986913517","https://openalex.org/W2463319298","https://openalex.org/W2062864035","https://openalex.org/W1496718033","https://openalex.org/W2053414040","https://openalex.org/W2995954300"],"abstract_inverted_index":{"The":[0,57],"known":[1],"theorems":[2],"by":[3],"E.A.":[4],"Barbashin":[5],"and":[6,13,81],"N.N.":[7],"Krasovskii":[8],"(1952)":[9],"about":[10],"the":[11,42,54,64,67,74,78,82,88],"asymptotic":[12],"global":[14],"stability":[15],"of":[16,24,53,63,70,77],"an":[17,21],"equilibrium":[18,43],"state":[19,44],"for":[20],"autonomous":[22],"system":[23,69],"differential":[25,31,79],"equations":[26],"are":[27,59],"extended":[28],"to":[29,51,73,87],"nonautonomous":[30],"inclusions":[32],"with":[33],"closed-valued":[34],"(but":[35],"not":[36],"necessarily":[37],"compact-valued)":[38],"right-hand":[39,75],"sides,":[40],"where":[41],"is":[45],"a":[46],"weakly":[47,83],"invariant":[48,84],"(with":[49],"respect":[50],"solutions":[52],"inclusion)":[55],"set.":[56],"statements":[58],"formulated":[60],"in":[61],"terms":[62],"Hausdorff-Bebutov":[65],"metric,":[66],"dynamical":[68],"translations":[71],"corresponding":[72,86],"side":[76],"inclusion,":[80],"set":[85],"inclusion.":[89]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-01T08:54:57.152042","created_date":"2016-06-24T00:00:00"}