{"id":"https://openalex.org/W2123800835","doi":"https://doi.org/10.1109/acc.2011.5990816","title":"A generalized Zames-Falb multiplier","display_name":"A generalized Zames-Falb multiplier","publication_year":2011,"publication_date":"2011-06-01","ids":{"openalex":"https://openalex.org/W2123800835","doi":"https://doi.org/10.1109/acc.2011.5990816","mag":"2123800835"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2011.5990816","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2011.5990816","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2011 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/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","Department of Electrical and Computer Engineering, University of Minnesota, 200 Union St. SE, 55455, Minneapolis, 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":"Department of Electrical and Computer Engineering, University of Minnesota, 200 Union St. SE, 55455, Minneapolis, 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","Department of Electrical and Computer Engineering, University of Minnesota, 200 Union St. SE, 55455, Minneapolis, 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":"Department of Electrical and Computer Engineering, University of Minnesota, 200 Union St. SE, 55455, Minneapolis, 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":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14832046,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":null,"first_page":"1990","last_page":"1993"},"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":0.9987000226974487,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9972000122070312,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.8022885322570801},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.685204029083252},{"id":"https://openalex.org/keywords/circle-criterion","display_name":"Circle criterion","score":0.6237860918045044},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5736989378929138},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5282126069068909},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4924260079860687},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4585530459880829},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.44595056772232056},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.4354557991027832},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4273829460144043},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.3296108841896057},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3145853877067566},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23762863874435425},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.11052197217941284},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10182052850723267}],"concepts":[{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.8022885322570801},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.685204029083252},{"id":"https://openalex.org/C65521940","wikidata":"https://www.wikidata.org/wiki/Q5121443","display_name":"Circle criterion","level":4,"score":0.6237860918045044},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5736989378929138},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5282126069068909},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4924260079860687},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4585530459880829},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.44595056772232056},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.4354557991027832},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4273829460144043},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.3296108841896057},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3145853877067566},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23762863874435425},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.11052197217941284},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10182052850723267},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2011.5990816","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2011.5990816","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2011 American Control Conference","raw_type":"proceedings-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/W2130394187","https://openalex.org/W2255439832","https://openalex.org/W2561646501","https://openalex.org/W6679560217"],"related_works":["https://openalex.org/W2077314575","https://openalex.org/W4315701745","https://openalex.org/W1990290471","https://openalex.org/W4380682190","https://openalex.org/W2005710836","https://openalex.org/W2102386043","https://openalex.org/W2945307361","https://openalex.org/W2116636209","https://openalex.org/W2053698688","https://openalex.org/W4362708037"],"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],"\"approximately\"":[66],"monotonic":[67],"odd.":[69],"This":[70],"result":[71],"extends":[72],"standard":[74],"an":[78],"additional":[79],"notion":[80],"\"robustness\".":[82]},"counts_by_year":[],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}