{"id":"https://openalex.org/W1963509687","doi":"https://doi.org/10.1137/120865173","title":"Lyapunov-like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems","display_name":"Lyapunov-like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1963509687","doi":"https://doi.org/10.1137/120865173","mag":"1963509687"},"language":"en","primary_location":{"id":"doi:10.1137/120865173","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120865173","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://pure.tue.nl/ws/files/3824902/566331847226211.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"A. N. Gorban","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"A. N. Gorban","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"I. Tyukin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"I. Tyukin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"E. Steur","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"E. Steur","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"H. Nijmeijer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"H. Nijmeijer","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5112,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.8360165,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"51","issue":"3","first_page":"2306","last_page":"2334"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.7656000256538391,"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":0.7656000256538391,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.038600001484155655,"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/T11525","display_name":"Piezoelectric Actuators and Control","score":0.032999999821186066,"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/convergence","display_name":"Convergence (economics)","score":0.6556000113487244},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.598800003528595},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.52920001745224},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4943000078201294},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.44339999556541443},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.35989999771118164},{"id":"https://openalex.org/keywords/uniform-convergence","display_name":"Uniform convergence","score":0.3562000095844269},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3476000130176544}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8353999853134155},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6556000113487244},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.598800003528595},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.52920001745224},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4943000078201294},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4810999929904938},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.44339999556541443},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.35989999771118164},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.3562000095844269},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3476000130176544},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.3416999876499176},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3294999897480011},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3068999946117401},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.2946000099182129},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.28040000796318054},{"id":"https://openalex.org/C52970973","wikidata":"https://www.wikidata.org/wiki/Q2497134","display_name":"Adaptive system","level":2,"score":0.2770000100135803},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C156387681","wikidata":"https://www.wikidata.org/wiki/Q6059484","display_name":"Invariance principle","level":2,"score":0.26350000500679016},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26080000400543213}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/120865173","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120865173","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:pure.tue.nl:publications/6353200a-8e12-4af7-8369-69cb350fdade","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/6353200a-8e12-4af7-8369-69cb350fdade","pdf_url":"https://pure.tue.nl/ws/files/3824902/566331847226211.pdf","source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Gorban, A N, Tyukin, I Y, Steur, E & Nijmeijer, H 2013, 'Lyapunov-like conditions of forward invariance and boundedness for a class of unstable systems', SIAM Journal on Control and Optimization, vol. 51, no. 3, pp. 2306-2334. https://doi.org/10.1137/120865173","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/412354","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/412354","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, vol. 51 (3), (2306-2334)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:0901.3577","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0901.3577","pdf_url":"https://arxiv.org/pdf/0901.3577","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:tue:oai:pure.tue.nl:publications/6353200a-8e12-4af7-8369-69cb350fdade","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/6353200a-8e12-4af7-8369-69cb350fdade","pdf_url":"https://research.tue.nl/nl/publications/6353200a-8e12-4af7-8369-69cb350fdade","source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 51(3), 2306 - 2334. Society for Industrial and Applied Mathematics (SIAM)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:pure.tue.nl:publications/6353200a-8e12-4af7-8369-69cb350fdade","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/6353200a-8e12-4af7-8369-69cb350fdade","pdf_url":"https://pure.tue.nl/ws/files/3824902/566331847226211.pdf","source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Gorban, A N, Tyukin, I Y, Steur, E & Nijmeijer, H 2013, 'Lyapunov-like conditions of forward invariance and boundedness for a class of unstable systems', SIAM Journal on Control and Optimization, vol. 51, no. 3, pp. 2306-2334. https://doi.org/10.1137/120865173","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1963509687.pdf","grobid_xml":"https://content.openalex.org/works/W1963509687.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W124300260","https://openalex.org/W1979563540","https://openalex.org/W1982138679","https://openalex.org/W1983918081","https://openalex.org/W1985940938","https://openalex.org/W1995553186","https://openalex.org/W2010242617","https://openalex.org/W2032489268","https://openalex.org/W2043493947","https://openalex.org/W2045938917","https://openalex.org/W2056751949","https://openalex.org/W2083848788","https://openalex.org/W2091926965","https://openalex.org/W2133330157","https://openalex.org/W2139686351","https://openalex.org/W2144684177","https://openalex.org/W2156687620","https://openalex.org/W2175510763","https://openalex.org/W2313800697"],"related_works":[],"abstract_inverted_index":{"We":[0],"provide":[1],"Lyapunov-like":[2],"characterizations":[3,105],"of":[4,8,14,21,31,43,49,73,83,112,124,127],"boundedness":[5,62],"and":[6,55,63],"convergence":[7,64,95,113],"nontrivial":[9],"solutions":[10,78],"for":[11,106],"a":[12,80],"class":[13],"systems":[15,22],"with":[16,34,119,130],"unstable":[17,36,98],"invariant":[18],"sets.":[19],"Examples":[20],"to":[23,60,70,77,91],"which":[24],"the":[25,66,84,107,122],"results":[26,67,101,116],"may":[27],"apply":[28],"include":[29],"interconnections":[30],"stable":[32,40,108],"subsystems":[33],"one-dimensional":[35],"dynamics":[37],"or":[38],"critically":[39],"dynamics.":[41],"Systems":[42],"this":[44],"type":[45],"arise":[46],"in":[47,97],"problems":[48],"nonlinear":[50],"output":[51],"regulation,":[52],"parameter":[53],"estimation,":[54],"adaptive":[56],"control.":[57],"In":[58,89],"addition":[59],"providing":[61],"criteria,":[65],"allow":[68],"us":[69],"derive":[71],"domains":[72],"initial":[74],"conditions":[75],"corresponding":[76],"leaving":[79],"given":[81],"neighborhood":[82],"origin":[85],"at":[86],"least":[87],"once.":[88],"contrast":[90],"other":[92],"works":[93],"addressing":[94],"issues":[96],"systems,":[99],"our":[100],"require":[102],"neither":[103],"input-output":[104],"part":[109],"nor":[110],"estimates":[111],"rates.":[114],"The":[115],"are":[117],"illustrated":[118],"examples,":[120],"including":[121],"analysis":[123],"phase":[125],"synchronization":[126],"neural":[128],"oscillators":[129],"heterogeneous":[131],"coupling.":[132]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2016-06-24T00:00:00"}
