{"id":"https://openalex.org/W2017942945","doi":"https://doi.org/10.1080/00207170701561427","title":"Fliess series, a generalization of the Ree's theorem, and an algebraic approach to a homogeneous approximation problem","display_name":"Fliess series, a generalization of the Ree's theorem, and an algebraic approach to a homogeneous approximation problem","publication_year":2008,"publication_date":"2008-03-01","ids":{"openalex":"https://openalex.org/W2017942945","doi":"https://doi.org/10.1080/00207170701561427","mag":"2017942945"},"language":"en","primary_location":{"id":"doi:10.1080/00207170701561427","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170701561427","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"},"type":"article","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/A5014476406","display_name":"Grigory M. Sklyar","orcid":"https://orcid.org/0000-0003-4588-9926"},"institutions":[{"id":"https://openalex.org/I104588304","display_name":"University of Szczecin","ror":"https://ror.org/05vmz5070","country_code":"PL","type":"education","lineage":["https://openalex.org/I104588304"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"G. M. Sklyar","raw_affiliation_strings":["Institute of Mathematics, University of Szczecin, Szczecin ,  Poland","Institute of Mathematics, University of Szczecin, Szczecin, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Szczecin, Szczecin ,  Poland","institution_ids":["https://openalex.org/I104588304"]},{"raw_affiliation_string":"Institute of Mathematics, University of Szczecin, Szczecin, Poland","institution_ids":["https://openalex.org/I104588304"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037179678","display_name":"S. Yu. Ignatovich","orcid":"https://orcid.org/0000-0003-2272-8644"},"institutions":[{"id":"https://openalex.org/I4210160820","display_name":"Kharkov Technologies","ror":"https://ror.org/0568rcd29","country_code":"UA","type":"company","lineage":["https://openalex.org/I4210160820"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"S. Y. Ignatovich","raw_affiliation_strings":["Department of Differential Equations and Control ,  Kharkov National University , Kharkov,  Ukraine","Department of Differential Equations and Control , Kharkov National University , Kharkov, Ukraine"],"affiliations":[{"raw_affiliation_string":"Department of Differential Equations and Control ,  Kharkov National University , Kharkov,  Ukraine","institution_ids":["https://openalex.org/I4210160820"]},{"raw_affiliation_string":"Department of Differential Equations and Control , Kharkov National University , Kharkov, Ukraine","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014476406"],"corresponding_institution_ids":["https://openalex.org/I104588304"],"apc_list":null,"apc_paid":null,"fwci":3.29,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.91975094,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"81","issue":"3","first_page":"371","last_page":"380"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.9726999998092651,"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"}},"topics":[{"id":"https://openalex.org/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.9726999998092651,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9724000096321106,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9695000052452087,"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/generalization","display_name":"Generalization","score":0.7740731239318848},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7008867859840393},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.6239888072013855},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6035818457603455},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5860083699226379},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5582606792449951},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.5465916395187378},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5445518493652344},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5385236740112305},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5170027017593384},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.47998377680778503},{"id":"https://openalex.org/keywords/lie-algebra","display_name":"Lie algebra","score":0.4550448954105377},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4220423698425293},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.21564191579818726},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15924406051635742},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06514650583267212}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7740731239318848},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7008867859840393},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.6239888072013855},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6035818457603455},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5860083699226379},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5582606792449951},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.5465916395187378},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5445518493652344},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5385236740112305},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5170027017593384},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.47998377680778503},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.4550448954105377},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4220423698425293},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.21564191579818726},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15924406051635742},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06514650583267212},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207170701561427","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170701561427","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W82099249","https://openalex.org/W91466345","https://openalex.org/W137071685","https://openalex.org/W390822549","https://openalex.org/W609406456","https://openalex.org/W1493137254","https://openalex.org/W1532177615","https://openalex.org/W1997139296","https://openalex.org/W2004847331","https://openalex.org/W2005873971","https://openalex.org/W2006740569","https://openalex.org/W2008695940","https://openalex.org/W2033536852","https://openalex.org/W2063532086","https://openalex.org/W2070267857","https://openalex.org/W2071120444","https://openalex.org/W2073710556","https://openalex.org/W2074884967","https://openalex.org/W2078359100","https://openalex.org/W2143810732","https://openalex.org/W2176339628","https://openalex.org/W2180949094","https://openalex.org/W2321285931","https://openalex.org/W2584784847","https://openalex.org/W4388320797","https://openalex.org/W6630746003"],"related_works":["https://openalex.org/W587735977","https://openalex.org/W1978142926","https://openalex.org/W3157395178","https://openalex.org/W184455116","https://openalex.org/W2028768252","https://openalex.org/W2371558776","https://openalex.org/W2045569473","https://openalex.org/W2364426643","https://openalex.org/W2399388599","https://openalex.org/W1571672327"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"an":[3],"algebraic":[4],"technique":[5],"originated":[6],"by":[7,29],"M.":[8],"Fliess":[9],"is":[10,27],"developed":[11],"and":[12,43],"applied":[13],"to":[14],"a":[15,30,38,49],"homogeneous":[16],"approximation":[17],"problem":[18],"for":[19],"nonlinear":[20],"affine":[21],"control":[22],"systems.":[23],"The":[24],"central":[25],"role":[26],"played":[28],"generalization":[31],"of":[32,40],"the":[33,44],"R.":[34],"Ree's":[35],"theorem":[36],"on":[37],"connection":[39],"Lie":[41],"elements":[42],"shuffle":[45],"product":[46],"operation":[47],"in":[48],"free":[50],"associative":[51],"algebra.":[52]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":31},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}