{"id":"https://openalex.org/W4220868607","doi":"https://doi.org/10.1007/s00500-022-06958-4","title":"A necessary and sufficient condition for the stability of interval difference equation via interval Lyapunov equation","display_name":"A necessary and sufficient condition for the stability of interval difference equation via interval Lyapunov equation","publication_year":2022,"publication_date":"2022-03-26","ids":{"openalex":"https://openalex.org/W4220868607","doi":"https://doi.org/10.1007/s00500-022-06958-4"},"language":"en","primary_location":{"id":"doi:10.1007/s00500-022-06958-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00500-022-06958-4","pdf_url":null,"source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11449/234331","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041196097","display_name":"Jos\u00e9 Renato Campos","orcid":"https://orcid.org/0000-0002-6490-6464"},"institutions":[{"id":"https://openalex.org/I107371206","display_name":"Federal Institute of S\u00e3o Paulo","ror":"https://ror.org/005pn5z34","country_code":"BR","type":"education","lineage":["https://openalex.org/I107371206"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 Renato Campos","raw_affiliation_strings":["Area of Sciences, Federal Institute of Education, Science and Technology of S\u00e3o Paulo, Votuporanga, SP, 15.503-110, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-6490-6464","affiliations":[{"raw_affiliation_string":"Area of Sciences, Federal Institute of Education, Science and Technology of S\u00e3o Paulo, Votuporanga, SP, 15.503-110, Brazil","institution_ids":["https://openalex.org/I107371206"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013377762","display_name":"Edvaldo Assun\u00e7\u00e3o","orcid":"https://orcid.org/0000-0002-4439-8570"},"institutions":[{"id":"https://openalex.org/I879563668","display_name":"Universidade Estadual Paulista (Unesp)","ror":"https://ror.org/00987cb86","country_code":"BR","type":"education","lineage":["https://openalex.org/I879563668"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Edvaldo Assun\u00e7\u00e3o","raw_affiliation_strings":["School of Engineering, S\u00e3o Paulo State University (UNESP), Ilha Solteira, SP, 15.385-000, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering, S\u00e3o Paulo State University (UNESP), Ilha Solteira, SP, 15.385-000, Brazil","institution_ids":["https://openalex.org/I879563668"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029082681","display_name":"Geraldo Nunes Silva","orcid":"https://orcid.org/0000-0002-3574-9893"},"institutions":[{"id":"https://openalex.org/I879563668","display_name":"Universidade Estadual Paulista (Unesp)","ror":"https://ror.org/00987cb86","country_code":"BR","type":"education","lineage":["https://openalex.org/I879563668"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Geraldo Nunes Silva","raw_affiliation_strings":["Institute of Biosciences, Humanities and Exact Sciences, S\u00e3o Paulo State University (UNESP), S\u00e3o Jos\u00e9 do Rio Preto, SP, 15.054-000, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Biosciences, Humanities and Exact Sciences, S\u00e3o Paulo State University (UNESP), S\u00e3o Jos\u00e9 do Rio Preto, SP, 15.054-000, Brazil","institution_ids":["https://openalex.org/I879563668"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090232242","display_name":"Weldon A. Lodwick","orcid":"https://orcid.org/0000-0003-0606-5916"},"institutions":[{"id":"https://openalex.org/I921990950","display_name":"University of Colorado Denver","ror":"https://ror.org/02hh7en24","country_code":"US","type":"education","lineage":["https://openalex.org/I921990950"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Weldon Alexander Lodwick","raw_affiliation_strings":["Department of Mathematical and Statistical Sciences, University of Colorado, Denver, CO, 80204, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical and Statistical Sciences, University of Colorado, Denver, CO, 80204, USA","institution_ids":["https://openalex.org/I921990950"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062045522","display_name":"Ulcilea Alves Severino Leal","orcid":"https://orcid.org/0000-0001-8586-1616"},"institutions":[{"id":"https://openalex.org/I4210106570","display_name":"Universidade Federal do Tri\u00e2ngulo Mineiro","ror":"https://ror.org/01av3m334","country_code":"BR","type":"education","lineage":["https://openalex.org/I4210106570"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Ulcilea Alves Severino Leal","raw_affiliation_strings":["Department of Mathematical, Federal University of Tri\u00e2ngulo Mineiro, Iturama, MG, 38.280-000, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical, Federal University of Tri\u00e2ngulo Mineiro, Iturama, MG, 38.280-000, Brazil","institution_ids":["https://openalex.org/I4210106570"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.7356,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.70522739,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"26","issue":"11","first_page":"5043","last_page":"5056"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11236","display_name":"Control Systems and Identification","score":0.9908000230789185,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9825999736785889,"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/interval","display_name":"Interval (graph theory)","score":0.7002159953117371},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6351872682571411},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5819897651672363},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4510388970375061},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.43548229336738586},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4257640242576599},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.3737430274486542},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.342396080493927},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2369646430015564},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.17488452792167664},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13888949155807495},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.063161700963974},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.05416885018348694},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.053009361028671265}],"concepts":[{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.7002159953117371},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6351872682571411},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5819897651672363},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4510388970375061},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.43548229336738586},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4257640242576599},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.3737430274486542},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.342396080493927},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2369646430015564},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.17488452792167664},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13888949155807495},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.063161700963974},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.05416885018348694},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.053009361028671265},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00500-022-06958-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00500-022-06958-4","pdf_url":null,"source":{"id":"https://openalex.org/S65753830","display_name":"Soft Computing","issn_l":"1432-7643","issn":["1432-7643","1433-7479"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Soft Computing","raw_type":"journal-article"},{"id":"pmh:oai:repositorio.unesp.br:11449/234331","is_oa":true,"landing_page_url":"http://hdl.handle.net/11449/234331","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"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":"instacron:UNESP","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:repositorio.unesp.br:11449/234331","is_oa":true,"landing_page_url":"http://hdl.handle.net/11449/234331","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"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":"instacron:UNESP","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4639900407","display_name":null,"funder_award_id":"400754/2014-2","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G5776357505","display_name":null,"funder_award_id":"301227/2017-9","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W98520975","https://openalex.org/W190239871","https://openalex.org/W1507872748","https://openalex.org/W1522916005","https://openalex.org/W1967231248","https://openalex.org/W2015136438","https://openalex.org/W2019778661","https://openalex.org/W2034038007","https://openalex.org/W2066745330","https://openalex.org/W2130751631","https://openalex.org/W2164821119","https://openalex.org/W2577829518","https://openalex.org/W2675961628","https://openalex.org/W2766160480","https://openalex.org/W2775179888","https://openalex.org/W2791285025","https://openalex.org/W2944501447","https://openalex.org/W3011474142","https://openalex.org/W3035983843","https://openalex.org/W3044378270","https://openalex.org/W3096950809","https://openalex.org/W4234521054","https://openalex.org/W4251446124","https://openalex.org/W4298255709"],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W2383986032","https://openalex.org/W2030955003","https://openalex.org/W2374426356","https://openalex.org/W1977987201","https://openalex.org/W2059628530","https://openalex.org/W2164487476","https://openalex.org/W3194517843","https://openalex.org/W2106169668","https://openalex.org/W2534107666"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
