{"id":"https://openalex.org/W3178467133","doi":"https://doi.org/10.1109/tac.2021.3095418","title":"Duality Bounds for Discrete-Time Zames\u2013Falb Multipliers","display_name":"Duality Bounds for Discrete-Time Zames\u2013Falb Multipliers","publication_year":2021,"publication_date":"2021-07-07","ids":{"openalex":"https://openalex.org/W3178467133","doi":"https://doi.org/10.1109/tac.2021.3095418","mag":"3178467133"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2021.3095418","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3095418","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/A5024598709","display_name":"Jingfan Zhang","orcid":"https://orcid.org/0000-0003-3082-1750"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Jingfan Zhang","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, School of Engineering, The University of Manchester, Manchester, U.K"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, School of Engineering, The University of Manchester, Manchester, U.K","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024320684","display_name":"Joaqu\u00edn Carrasco","orcid":"https://orcid.org/0000-0002-7499-6408"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Joaquin Carrasco","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, School of Engineering, The University of Manchester, Manchester, U.K"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, School of Engineering, The University of Manchester, Manchester, U.K","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078717262","display_name":"William P. Heath","orcid":"https://orcid.org/0000-0003-0016-8105"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"William Paul Heath","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, School of Engineering, The University of Manchester, Manchester, U.K"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, School of Engineering, The University of Manchester, Manchester, U.K","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5024598709"],"corresponding_institution_ids":["https://openalex.org/I28407311"],"apc_list":null,"apc_paid":null,"fwci":4.9157,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.95598349,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"67","issue":"7","first_page":"3521","last_page":"3528"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9943000078201294,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9943000078201294,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9918000102043152,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.9916999936103821,"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/multiplier","display_name":"Multiplier (economics)","score":0.7332618236541748},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.705318808555603},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6515202522277832},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.5971046090126038},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.45364829897880554},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4384559690952301},{"id":"https://openalex.org/keywords/discrete-system","display_name":"Discrete system","score":0.42532384395599365},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4086756408214569},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.30677181482315063},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.19990909099578857},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19453123211860657}],"concepts":[{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.7332618236541748},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.705318808555603},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6515202522277832},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.5971046090126038},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.45364829897880554},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4384559690952301},{"id":"https://openalex.org/C96314035","wikidata":"https://www.wikidata.org/wiki/Q5282062","display_name":"Discrete system","level":2,"score":0.42532384395599365},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4086756408214569},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30677181482315063},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.19990909099578857},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19453123211860657},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2021.3095418","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3095418","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":[{"id":"https://openalex.org/G5391253235","display_name":null,"funder_award_id":"EP/S03286X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5564952769","display_name":"Digital twin-based Bilateral Teleautonomous System for Nuclear Remote Operation","funder_award_id":"EP/S03286X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320291","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W1481269173","https://openalex.org/W1649291105","https://openalex.org/W1691404827","https://openalex.org/W1811601109","https://openalex.org/W1813780083","https://openalex.org/W1921365937","https://openalex.org/W2023285936","https://openalex.org/W2026769037","https://openalex.org/W2029731417","https://openalex.org/W2061360635","https://openalex.org/W2063493327","https://openalex.org/W2075887963","https://openalex.org/W2078130230","https://openalex.org/W2084233036","https://openalex.org/W2097460613","https://openalex.org/W2099090022","https://openalex.org/W2101330244","https://openalex.org/W2112250396","https://openalex.org/W2112446957","https://openalex.org/W2112822418","https://openalex.org/W2114355944","https://openalex.org/W2117158142","https://openalex.org/W2121768877","https://openalex.org/W2125768404","https://openalex.org/W2129713275","https://openalex.org/W2134456514","https://openalex.org/W2149249236","https://openalex.org/W2152522362","https://openalex.org/W2160990899","https://openalex.org/W2170167406","https://openalex.org/W2172230749","https://openalex.org/W2187099408","https://openalex.org/W2268709424","https://openalex.org/W2343951720","https://openalex.org/W2408541880","https://openalex.org/W2547940578","https://openalex.org/W2605567118","https://openalex.org/W2903148209","https://openalex.org/W2962918072","https://openalex.org/W2964102336","https://openalex.org/W3011830603","https://openalex.org/W3044597058","https://openalex.org/W3083691206","https://openalex.org/W3106275197","https://openalex.org/W3112645287","https://openalex.org/W3123508376","https://openalex.org/W3164762521","https://openalex.org/W3178467133","https://openalex.org/W4205241083","https://openalex.org/W4205625716","https://openalex.org/W4244799121","https://openalex.org/W6782726895","https://openalex.org/W7052509659"],"related_works":["https://openalex.org/W3213165575","https://openalex.org/W2406638882","https://openalex.org/W2391797119","https://openalex.org/W4307261727","https://openalex.org/W2136200239","https://openalex.org/W2080941243","https://openalex.org/W2362763982","https://openalex.org/W4283709143","https://openalex.org/W4224273196","https://openalex.org/W2038258422"],"abstract_inverted_index":{"This":[0],"note":[1],"presents":[2],"phase":[3,43,69],"conditions":[4,20,31],"under":[5],"which":[6,119],"there":[7],"is":[8,102,126],"no":[9],"suitable":[10,121],"Zames\u2013":[11,122],"Falb":[12,123],"multiplier":[13,124],"for":[14,32,99,118],"a":[15,64,120],"given":[16],"discrete-time":[17,26],"system.":[18],"Our":[19],"can":[21,55,78],"be":[22,56],"seen":[23],"as":[24],"the":[25,46,74,94,114],"counterpart":[27],"of":[28,116],"J\u00f6nsson\u2019s":[29],"duality":[30],"Zames\u2013Falb":[33,100],"multipliers.":[34],"By":[35],"contrast":[36],"with":[37,84],"their":[38],"continuous-time":[39],"counterparts":[40],"and":[41],"other":[42],"limitations":[44,70],"in":[45,59,73,97],"literature,":[47],"they":[48,106],"lead":[49],"to":[50,91,109],"numerically":[51],"efficient":[52],"results":[53,88],"that":[54,76,81,93,113],"computed":[57],"either":[58],"closed":[60],"form":[61],"or":[62],"via":[63],"linear":[65],"program.":[66],"The":[67,86],"closed-form":[68],"are":[71],"tight":[72],"sense":[75],"we":[77],"construct":[79],"multipliers":[80,101],"meet":[82],"them":[83],"equality.":[85],"numerical":[87],"allow":[89,107],"us":[90,108],"conclude":[92],"current":[95],"state-of-the-art":[96],"searches":[98],"not":[103],"conservative.":[104],"Moreover,":[105],"show,":[110],"by":[111],"construction,":[112],"set":[115],"plants":[117],"exists":[125],"nonconvex.":[127]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
