{"id":"https://openalex.org/W2114355944","doi":"https://doi.org/10.1109/tac.2011.2112450","title":"A Generalized Zames-Falb Multiplier","display_name":"A Generalized Zames-Falb Multiplier","publication_year":2011,"publication_date":"2011-02-09","ids":{"openalex":"https://openalex.org/W2114355944","doi":"https://doi.org/10.1109/tac.2011.2112450","mag":"2114355944"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2011.2112450","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2011.2112450","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/A5058663513","display_name":"Donatello Materassi","orcid":"https://orcid.org/0000-0002-4736-8377"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Donatello Materassi","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA","Dept. of Electr. & Comput. Eng, Univ. of Minnesota, Minneapolis, MN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng, Univ. of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069864205","display_name":"Murti V. Salapaka","orcid":"https://orcid.org/0000-0002-4595-9683"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Murti V. Salapaka","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA","Dept. of Electr. & Comput. Eng, Univ. of Minnesota, Minneapolis, MN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng, Univ. of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I130238516"],"apc_list":null,"apc_paid":null,"fwci":3.2861,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.926381,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"56","issue":"6","first_page":"1432","last_page":"1436"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9995999932289124,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9995999932289124,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9993000030517578,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9980000257492065,"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/monotonic-function","display_name":"Monotonic function","score":0.7896578907966614},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.692240834236145},{"id":"https://openalex.org/keywords/circle-criterion","display_name":"Circle criterion","score":0.6688105463981628},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5992472171783447},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5470359325408936},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5467190146446228},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4899524748325348},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46673783659935},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.46220847964286804},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.46038341522216797},{"id":"https://openalex.org/keywords/nonlinear-control","display_name":"Nonlinear control","score":0.4486517906188965},{"id":"https://openalex.org/keywords/describing-function","display_name":"Describing function","score":0.44465261697769165},{"id":"https://openalex.org/keywords/control-system","display_name":"Control system","score":0.4300379753112793},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.2877430021762848},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2628486752510071},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23318925499916077},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.13025563955307007},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09834885597229004},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.09283223748207092}],"concepts":[{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.7896578907966614},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.692240834236145},{"id":"https://openalex.org/C65521940","wikidata":"https://www.wikidata.org/wiki/Q5121443","display_name":"Circle criterion","level":4,"score":0.6688105463981628},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5992472171783447},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5470359325408936},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5467190146446228},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4899524748325348},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46673783659935},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.46220847964286804},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.46038341522216797},{"id":"https://openalex.org/C91581856","wikidata":"https://www.wikidata.org/wiki/Q2707001","display_name":"Nonlinear control","level":3,"score":0.4486517906188965},{"id":"https://openalex.org/C147317941","wikidata":"https://www.wikidata.org/wiki/Q1925419","display_name":"Describing function","level":3,"score":0.44465261697769165},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.4300379753112793},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.2877430021762848},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2628486752510071},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23318925499916077},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.13025563955307007},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09834885597229004},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09283223748207092},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2011.2112450","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2011.2112450","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W2009253901","https://openalex.org/W2011492128","https://openalex.org/W2053307451","https://openalex.org/W2061356889","https://openalex.org/W2068703754","https://openalex.org/W2077418568","https://openalex.org/W2086101645","https://openalex.org/W2097944741","https://openalex.org/W2101330244","https://openalex.org/W2120036139","https://openalex.org/W2127845920","https://openalex.org/W2130394187","https://openalex.org/W2255439832","https://openalex.org/W6679560217"],"related_works":["https://openalex.org/W1559014088","https://openalex.org/W2149571926","https://openalex.org/W2068619682","https://openalex.org/W4387276406","https://openalex.org/W1981564162","https://openalex.org/W2011492128","https://openalex.org/W4210283992","https://openalex.org/W1496660757","https://openalex.org/W2148909886","https://openalex.org/W2053242429"],"abstract_inverted_index":{"Lur'e":[0,27,58],"systems":[1],"represent":[2],"feedback":[3],"interconnections":[4],"of":[5,25,47,54,56,81],"a":[6,11,18,26,36,45,57],"Linear":[7],"Time-Invariant":[8],"system":[9,28,59],"with":[10,77],"nonlinear":[12,31,61],"operator.":[13],"The":[14,42],"Zames-Falb":[15,49,75],"criterion":[16,50,76],"is":[17,33],"powerful":[19],"tool":[20],"to":[21],"determine":[22],"the":[23,30,48,52,73],"stability":[24,55],"when":[29],"operator":[32],"defined":[34],"by":[35],"monotonic,":[37],"odd":[38],"and":[39,68],"single-valued":[40],"function.":[41],"article":[43],"provides":[44],"generalization":[46],"for":[51,60],"analysis":[53],"static":[62],"operators":[63],"that":[64],"are":[65],"\u201capproximately\u201d":[66],"monotonic":[67],"odd.":[69],"This":[70],"result":[71],"extends":[72],"standard":[74],"an":[78],"additional":[79],"notion":[80],"\u201crobustness\u201d.":[82]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
