{"id":"https://openalex.org/W2099869999","doi":"https://doi.org/10.1109/tac.2011.2170449","title":"Model Reduction for a Class of Convergent Nonlinear Systems","display_name":"Model Reduction for a Class of Convergent Nonlinear Systems","publication_year":2011,"publication_date":"2011-10-05","ids":{"openalex":"https://openalex.org/W2099869999","doi":"https://doi.org/10.1109/tac.2011.2170449","mag":"2099869999"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2011.2170449","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2011.2170449","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic 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/A5083507299","display_name":"Bart Besselink","orcid":"https://orcid.org/0000-0001-5194-3306"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"B. Besselink","raw_affiliation_strings":["Dynamics and Control group, Eindhoven University of Technology, Eindhoven, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dynamics and Control group, Eindhoven University of Technology, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004028181","display_name":"Nathan van de Wouw","orcid":"https://orcid.org/0000-0002-6745-9137"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"N. van de Wouw","raw_affiliation_strings":["Dynamics and Control group, Eindhoven University of Technology, Eindhoven, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dynamics and Control group, Eindhoven University of Technology, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022300438","display_name":"Henk Nijmeijer","orcid":"https://orcid.org/0000-0001-5883-6191"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"H. Nijmeijer","raw_affiliation_strings":["Dynamics and Control group, Eindhoven University of Technology, Eindhoven, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dynamics and Control group, Eindhoven University of Technology, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I83019370"],"apc_list":null,"apc_paid":null,"fwci":1.58,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.83276545,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"57","issue":"4","first_page":"1071","last_page":"1076"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T11372","display_name":"Hydraulic and Pneumatic Systems","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9941999912261963,"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/nonlinear-system","display_name":"Nonlinear system","score":0.798292875289917},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.7126882076263428},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6611351370811462},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.636384904384613},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6010935306549072},{"id":"https://openalex.org/keywords/interconnection","display_name":"Interconnection","score":0.5383113622665405},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4907432794570923},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4903848171234131},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4767250120639801},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.47166526317596436},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.42951279878616333},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4263843595981598},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4223605990409851},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3944162130355835},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22708597779273987},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.16508236527442932},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09790405631065369},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07517856359481812},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.06332632899284363},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05685001611709595}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.798292875289917},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.7126882076263428},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6611351370811462},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.636384904384613},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6010935306549072},{"id":"https://openalex.org/C123745756","wikidata":"https://www.wikidata.org/wiki/Q1665949","display_name":"Interconnection","level":2,"score":0.5383113622665405},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4907432794570923},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4903848171234131},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4767250120639801},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.47166526317596436},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.42951279878616333},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4263843595981598},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4223605990409851},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3944162130355835},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22708597779273987},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.16508236527442932},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09790405631065369},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07517856359481812},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.06332632899284363},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05685001611709595},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tac.2011.2170449","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2011.2170449","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/bafdafbf-74cd-4478-bc36-68e49349006b","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/bafdafbf-74cd-4478-bc36-68e49349006b","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Besselink, B, Wouw, van de, N & Nijmeijer, H 2012, 'Model reduction for a class of convergent nonlinear systems', IEEE Transactions on Automatic Control, vol. 57, no. 4, pp. 1071-1076. https://doi.org/10.1109/TAC.2011.2170449","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:719936","is_oa":false,"landing_page_url":"http://library.tue.nl/csp/dare/LinkToRepository.csp?recordnumber=719936","pdf_url":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:0018-9286","raw_type":"Article / Letter to the editor"},{"id":"pmh:oai:library.tue.nl:719936","is_oa":false,"landing_page_url":"http://repository.tue.nl/719936","pdf_url":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:0018-9286","raw_type":"Article / Letter to the editor"},{"id":"pmh:tue:oai:pure.tue.nl:publications/bafdafbf-74cd-4478-bc36-68e49349006b","is_oa":false,"landing_page_url":"https://research.tue.nl/nl/publications/bafdafbf-74cd-4478-bc36-68e49349006b","pdf_url":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, 57(4), 1071 - 1076. Institute of Electrical and Electronics Engineers","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W55814457","https://openalex.org/W1543420164","https://openalex.org/W1551480811","https://openalex.org/W1868559974","https://openalex.org/W1984714339","https://openalex.org/W2008663032","https://openalex.org/W2036826525","https://openalex.org/W2059602198","https://openalex.org/W2064733273","https://openalex.org/W2065313971","https://openalex.org/W2067070250","https://openalex.org/W2071861954","https://openalex.org/W2079665343","https://openalex.org/W2099869999","https://openalex.org/W2103960654","https://openalex.org/W2115424783","https://openalex.org/W2117079884","https://openalex.org/W2133642820","https://openalex.org/W2138190945","https://openalex.org/W2154930603","https://openalex.org/W2163439281","https://openalex.org/W2165808313","https://openalex.org/W2312915715"],"related_works":["https://openalex.org/W2155019192","https://openalex.org/W2014709025","https://openalex.org/W4249035840","https://openalex.org/W2766970861","https://openalex.org/W3125341812","https://openalex.org/W1668171714","https://openalex.org/W4380607112","https://openalex.org/W2218294330","https://openalex.org/W1997278405","https://openalex.org/W2347989876"],"abstract_inverted_index":{"In":[0],"this":[1],"technical":[2],"note,":[3],"a":[4,18,22,68],"model":[5,33],"reduction":[6],"procedure":[7],"is":[8,45],"presented":[9],"for":[10,28],"nonlinear":[11,25,69],"systems":[12],"that":[13],"can":[14],"be":[15,50],"decomposed":[16],"into":[17],"feedback":[19],"interconnection":[20],"of":[21,30,57],"linear":[23],"and":[24,34,55],"subsystem.":[26],"Conditions":[27],"stability":[29],"the":[31,41,53,58],"reduced-order":[32],"an":[35],"error":[36,59],"bound":[37],"are":[38,63],"given.":[39],"Herein,":[40],"input-to-state":[42],"convergence":[43],"property":[44],"exploited,":[46],"which":[47],"proves":[48],"to":[49,67],"useful":[51],"in":[52],"definition":[54],"derivation":[56],"bound.":[60],"The":[61],"results":[62],"illustrated":[64],"by":[65],"application":[66],"mechanical":[70],"system.":[71]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}