{"id":"https://openalex.org/W2159293839","doi":"https://doi.org/10.1109/acc.2007.4282579","title":"A Sum of Squares Approach to Stability Analysis of Polynomial Fuzzy Systems","display_name":"A Sum of Squares Approach to Stability Analysis of Polynomial Fuzzy Systems","publication_year":2007,"publication_date":"2007-07-01","ids":{"openalex":"https://openalex.org/W2159293839","doi":"https://doi.org/10.1109/acc.2007.4282579","mag":"2159293839"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2007.4282579","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4282579","pdf_url":null,"source":{"id":"https://openalex.org/S4210168941","display_name":"Proceedings of the ... American Control Conference/Proceedings of the American Control Conference","issn_l":"0743-1619","issn":["0743-1619","2378-5861"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","raw_type":"proceedings-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/A5110036639","display_name":"Kazuo Tanaka","orcid":null},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Kazuo Tanaka","raw_affiliation_strings":["Department of Mechanical Systems and Intelligent Systems, University of Electro-Communications, Chofu, Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Systems and Intelligent Systems, University of Electro-Communications, Chofu, Tokyo, Japan","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054639429","display_name":"Hiroto Yoshida","orcid":"https://orcid.org/0000-0001-6890-4397"},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hiroto Yoshida","raw_affiliation_strings":["Department of Mechanical Systems and Intelligent Systems, University of Electro-Communications, Chofu, Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Systems and Intelligent Systems, University of Electro-Communications, Chofu, Tokyo, Japan","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113663849","display_name":"Hiroshi Ohtake","orcid":null},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hiroshi Ohtake","raw_affiliation_strings":["Department of Mechanical Systems and Intelligent Systems, University of Electro-Communications, Chofu, Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Systems and Intelligent Systems, University of Electro-Communications, Chofu, Tokyo, Japan","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082136205","display_name":"Hua O. Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I111088046","display_name":"Boston University","ror":"https://ror.org/05qwgg493","country_code":"US","type":"education","lineage":["https://openalex.org/I111088046"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hua O. Wang","raw_affiliation_strings":["Department of Aerospace and Mechanical Engineering, Boston University, Boston, MA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Aerospace and Mechanical Engineering, Boston University, Boston, MA, USA","institution_ids":["https://openalex.org/I111088046"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5110036639"],"corresponding_institution_ids":["https://openalex.org/I20529979"],"apc_list":null,"apc_paid":null,"fwci":7.6113,"has_fulltext":false,"cited_by_count":93,"citation_normalized_percentile":{"value":0.97964722,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"4071","last_page":"4076"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9606000185012817,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9587000012397766,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/explained-sum-of-squares","display_name":"Explained sum of squares","score":0.6841894388198853},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6314737796783447},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6022226214408875},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6002153754234314},{"id":"https://openalex.org/keywords/fuzzy-control-system","display_name":"Fuzzy control system","score":0.5962338447570801},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.559242308139801},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5563266277313232},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5535531044006348},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4664888381958008},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4571636915206909},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.45276087522506714},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4450162649154663},{"id":"https://openalex.org/keywords/stability-conditions","display_name":"Stability conditions","score":0.43423426151275635},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4052850604057312},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3825286030769348},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30471915006637573},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.15991467237472534},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1173909604549408},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.09359899163246155},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.053026944398880005}],"concepts":[{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.6841894388198853},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6314737796783447},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6022226214408875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6002153754234314},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.5962338447570801},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.559242308139801},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5563266277313232},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5535531044006348},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4664888381958008},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4571636915206909},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.45276087522506714},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4450162649154663},{"id":"https://openalex.org/C143170015","wikidata":"https://www.wikidata.org/wiki/Q17007850","display_name":"Stability conditions","level":3,"score":0.43423426151275635},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4052850604057312},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3825286030769348},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30471915006637573},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.15991467237472534},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1173909604549408},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.09359899163246155},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.053026944398880005},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2007.4282579","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4282579","pdf_url":null,"source":{"id":"https://openalex.org/S4210168941","display_name":"Proceedings of the ... American Control Conference/Proceedings of the American Control Conference","issn_l":"0743-1619","issn":["0743-1619","2378-5861"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1548148540","https://openalex.org/W2049087128","https://openalex.org/W2079325629","https://openalex.org/W2130795193","https://openalex.org/W2133404041","https://openalex.org/W2162098902","https://openalex.org/W2164484193","https://openalex.org/W2178412471","https://openalex.org/W4213345774","https://openalex.org/W6684061903"],"related_works":["https://openalex.org/W2028806697","https://openalex.org/W2524522145","https://openalex.org/W2106144756","https://openalex.org/W2388496637","https://openalex.org/W2568163574","https://openalex.org/W2061897416","https://openalex.org/W2003652915","https://openalex.org/W1618149703","https://openalex.org/W3091119762","https://openalex.org/W2133961832"],"abstract_inverted_index":{"This":[0],"paper":[1,78],"presents":[2],"a":[3,37,43,69,153,169],"sum":[4],"of":[5,12,47,106,125,163],"squares":[6],"(SOS)":[7],"approach":[8,18,100,140,165],"to":[9,30,90],"stability":[10,56,73,95,144],"analysis":[11,74],"polynomial":[13,38,60,154],"fuzzy":[14,32,39,51,92],"systems.":[15,33,93],"Our":[16],"SOS":[17,107],"provides":[19,141],"two":[20,129],"innovative":[21],"and":[22,108,123,152],"extensive":[23],"results":[24,145],"for":[25],"the":[26,48,86,98,115,121,126,148,161],"existing":[27,87,149],"LMI":[28,88,150],"approaches":[29,89,151],"Takagi-Sugeno":[31,50,91],"First,":[34],"we":[35,54],"propose":[36],"model":[40],"that":[41,63,83,138],"is":[42,79],"more":[44,80,142],"general":[45,81],"representation":[46],"well-known":[49],"model.":[52],"Second,":[53],"derive":[55],"conditions":[57,96],"based":[58,84],"on":[59,85],"Lyapunov":[61,66,171],"functions":[62,67],"contain":[64],"quadratic":[65],"as":[68],"special":[70],"case.":[71],"Hence,":[72],"discussed":[75],"in":[76,97,104,166],"this":[77],"than":[82,146],"The":[94,134,157],"proposed":[99,127],"can":[101],"be":[102],"represented":[103],"terms":[105],"are":[109,132],"numerically":[110],"(partially":[111],"symbolically)":[112],"solved":[113],"via":[114],"recent":[116],"developed":[117],"SOSTOOLS.":[118],"To":[119],"illustrate":[120],"validity":[122],"applicability":[124],"approach,":[128],"analytical":[130],"examples":[131],"provided.":[133],"first":[135],"example":[136,159],"shows":[137],"our":[139,164],"relaxed":[143],"both":[147],"system":[155],"approach.":[156,173],"second":[158],"illustrates":[160],"utility":[162],"comparison":[167],"with":[168],"piecewise":[170],"function":[172]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
