{"id":"https://openalex.org/W4412973020","doi":"https://doi.org/10.1109/tac.2025.3590114","title":"Gain-Type and Phase-Type Multipliers for Feedback Robustness","display_name":"Gain-Type and Phase-Type Multipliers for Feedback Robustness","publication_year":2025,"publication_date":"2025-07-17","ids":{"openalex":"https://openalex.org/W4412973020","doi":"https://doi.org/10.1109/tac.2025.3590114"},"language":null,"primary_location":{"id":"doi:10.1109/tac.2025.3590114","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3590114","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/A5065282168","display_name":"Axel Ringh","orcid":"https://orcid.org/0000-0002-9778-1426"},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]},{"id":"https://openalex.org/I881427289","display_name":"University of Gothenburg","ror":"https://ror.org/01tm6cn81","country_code":"SE","type":"education","lineage":["https://openalex.org/I881427289"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Axel Ringh","raw_affiliation_strings":["Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden"],"raw_orcid":"https://orcid.org/0000-0002-9778-1426","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden","institution_ids":["https://openalex.org/I66862912","https://openalex.org/I881427289"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Xin Mao","orcid":"https://orcid.org/0000-0002-2801-9761"},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xin Mao","raw_affiliation_strings":["School of Data Science and Society, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA"],"raw_orcid":"https://orcid.org/0000-0002-2801-9761","affiliations":[{"raw_affiliation_string":"School of Data Science and Society, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA","institution_ids":["https://openalex.org/I114027177"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100344590","display_name":"Wei Chen","orcid":"https://orcid.org/0000-0003-4074-3100"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Chen","raw_affiliation_strings":["School of Advanced Manufacturing and Robotics and State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing, China","School of Advanced Manufacturing and Robotics & State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-4074-3100","affiliations":[{"raw_affiliation_string":"School of Advanced Manufacturing and Robotics and State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"School of Advanced Manufacturing and Robotics & State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065168162","display_name":"Li Qiu","orcid":"https://orcid.org/0000-0001-8218-9940"},"institutions":[{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Qiu","raw_affiliation_strings":["School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, China","School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Guangdong, China"],"raw_orcid":"https://orcid.org/0000-0001-8218-9940","affiliations":[{"raw_affiliation_string":"School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, China","institution_ids":["https://openalex.org/I4210116924"]},{"raw_affiliation_string":"School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Guangdong, China","institution_ids":["https://openalex.org/I4210116924"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023235121","display_name":"Sei Zhen Khong","orcid":"https://orcid.org/0000-0003-4735-5872"},"institutions":[{"id":"https://openalex.org/I142974352","display_name":"National Sun Yat-sen University","ror":"https://ror.org/00mjawt10","country_code":"TW","type":"education","lineage":["https://openalex.org/I142974352"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Sei Zhen Khong","raw_affiliation_strings":["Department of Electrical Engineering, National Sun Yat-sen University, Kaohsiung, Taiwan"],"raw_orcid":"https://orcid.org/0000-0003-4735-5872","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, National Sun Yat-sen University, Kaohsiung, Taiwan","institution_ids":["https://openalex.org/I142974352"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12232698,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"71","issue":"1","first_page":"291","last_page":"306"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10323","display_name":"Analog and Mixed-Signal Circuit Design","score":0.9729999899864197,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T10323","display_name":"Analog and Mixed-Signal Circuit Design","score":0.9729999899864197,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T11992","display_name":"CCD and CMOS Imaging Sensors","score":0.9248999953269958,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10369","display_name":"Advanced MEMS and NEMS Technologies","score":0.9088000059127808,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/robustness","display_name":"Robustness (evolution)","score":0.7178578972816467},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.7059679627418518},{"id":"https://openalex.org/keywords/feedback-control","display_name":"Feedback control","score":0.45129746198654175},{"id":"https://openalex.org/keywords/output-feedback","display_name":"Output feedback","score":0.4401536285877228},{"id":"https://openalex.org/keywords/robust-control","display_name":"Robust control","score":0.4253998398780823},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41334670782089233},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3800017237663269},{"id":"https://openalex.org/keywords/control-system","display_name":"Control system","score":0.29666802287101746},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.2306886613368988},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.18177369236946106},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.14876043796539307},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12701600790023804},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.07198834419250488},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.07123196125030518}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7178578972816467},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7059679627418518},{"id":"https://openalex.org/C3018651601","wikidata":"https://www.wikidata.org/wiki/Q183635","display_name":"Feedback control","level":2,"score":0.45129746198654175},{"id":"https://openalex.org/C3018623182","wikidata":"https://www.wikidata.org/wiki/Q154021","display_name":"Output feedback","level":3,"score":0.4401536285877228},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.4253998398780823},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41334670782089233},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3800017237663269},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.29666802287101746},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.2306886613368988},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.18177369236946106},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.14876043796539307},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12701600790023804},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.07198834419250488},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.07123196125030518},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2025.3590114","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3590114","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/G112952530","display_name":null,"funder_award_id":"72131001 and T2121002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1764963776","display_name":null,"funder_award_id":"KAW 2018.0349","funder_id":"https://openalex.org/F4320322327","funder_display_name":"Knut och Alice Wallenbergs Stiftelse"},{"id":"https://openalex.org/G2110271586","display_name":"Advanced Technology Development for Microgrids at Distribution Level: Prototype Design, Function Verification, and Field Testing( I )","funder_award_id":"NSTC114-2218-E007-011","funder_id":"https://openalex.org/F2461203286","funder_display_name":"National Science and Technology Council"},{"id":"https://openalex.org/G4941793921","display_name":null,"funder_award_id":"62073003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6341322007","display_name":"Negative Imaginary Systems Control Theory and Its Applications in Complex Flexible Structures","funder_award_id":"NSTC113-2222-E110-002-MY3","funder_id":"https://openalex.org/F2461203286","funder_display_name":"National Science and Technology Council"}],"funders":[{"id":"https://openalex.org/F2461203286","display_name":"National Science and Technology Council","ror":"https://ror.org/02kv4zf79"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322327","display_name":"Knut och Alice Wallenbergs Stiftelse","ror":"https://ror.org/004hzzk67"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":68,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1483804921","https://openalex.org/W1488435683","https://openalex.org/W1563898868","https://openalex.org/W1792735992","https://openalex.org/W1948872058","https://openalex.org/W1973866509","https://openalex.org/W1994930929","https://openalex.org/W1998990268","https://openalex.org/W2004470537","https://openalex.org/W2004485278","https://openalex.org/W2008334035","https://openalex.org/W2011745876","https://openalex.org/W2012430774","https://openalex.org/W2016657621","https://openalex.org/W2018779245","https://openalex.org/W2026601157","https://openalex.org/W2036286326","https://openalex.org/W2040172299","https://openalex.org/W2060405197","https://openalex.org/W2063493327","https://openalex.org/W2074999961","https://openalex.org/W2082475830","https://openalex.org/W2082483338","https://openalex.org/W2097114089","https://openalex.org/W2097460613","https://openalex.org/W2097944741","https://openalex.org/W2099076091","https://openalex.org/W2102330779","https://openalex.org/W2103313140","https://openalex.org/W2106901410","https://openalex.org/W2107543637","https://openalex.org/W2113642685","https://openalex.org/W2121768877","https://openalex.org/W2123173024","https://openalex.org/W2134840386","https://openalex.org/W2150883820","https://openalex.org/W2163229019","https://openalex.org/W2164105535","https://openalex.org/W2172866952","https://openalex.org/W2250342892","https://openalex.org/W2330286668","https://openalex.org/W2342631389","https://openalex.org/W2489446563","https://openalex.org/W2565271410","https://openalex.org/W2739569331","https://openalex.org/W2885943011","https://openalex.org/W2944865453","https://openalex.org/W2952104666","https://openalex.org/W3003231466","https://openalex.org/W3012261256","https://openalex.org/W3109930360","https://openalex.org/W3141780772","https://openalex.org/W3185021909","https://openalex.org/W3198137147","https://openalex.org/W4225376134","https://openalex.org/W4234984831","https://openalex.org/W4243620103","https://openalex.org/W4245345046","https://openalex.org/W4249104068","https://openalex.org/W4249669669","https://openalex.org/W4254315740","https://openalex.org/W4292058084","https://openalex.org/W4385308513","https://openalex.org/W4392939586","https://openalex.org/W4394571452","https://openalex.org/W4394944735","https://openalex.org/W4402389260"],"related_works":["https://openalex.org/W2153650151","https://openalex.org/W2334516743","https://openalex.org/W2486306719","https://openalex.org/W2106487132","https://openalex.org/W2369282358","https://openalex.org/W2482257683","https://openalex.org/W3022029778","https://openalex.org/W2019249007","https://openalex.org/W2800406697","https://openalex.org/W2139918612"],"abstract_inverted_index":{"It":[0],"is":[1,28,59,82,96,130],"known":[2,33],"that":[3,16,44,55,72,95],"the":[4,17,20,35,45,57,80,109,122,128,155,168,172],"stability":[5],"of":[6,10,19,39,97,111,113,124],"a":[7,70,74,92,140,158],"feedback":[8,58,81,129],"interconnection":[9],"two":[11],"linear":[12],"time-invariant":[13],"systems":[14,22],"implies":[15],"graphs":[18],"open-loop":[21],"are":[23,103,147,151],"quadratically":[24],"separated.":[25],"This":[26,52],"separation":[27],"defined":[29],"by":[30],"an":[31],"object":[32],"as":[34],"multiplier.":[36],"The":[37,149],"theory":[38],"integral":[40],"quadratic":[41],"constraints":[42],"shows":[43],"converse":[46],"also":[47],"holds":[48],"under":[49],"certain":[50,63,86,134],"conditions.":[51],"paper":[53],"establishes":[54],"if":[56,79,127],"robustly":[60,83,131],"stable":[61,84,132],"against":[62],"structured":[64],"uncertainty,":[65,88,136],"then":[66,89,137],"there":[67,90,138],"always":[68],"exists":[69,91,139],"multiplier":[71,94,160],"takes":[73],"corresponding":[75,93],"form.":[76],"In":[77],"particular,":[78],"to":[85,133],"gain-type":[87,141],"phase-type,":[98],"i.e.,":[99,143],"its":[100,144],"diagonal":[101],"blocks":[102,146],"zeros.":[104,148],"These":[105],"results":[106,150],"build":[107],"on":[108],"notion":[110],"phases":[112],"matrices":[114],"and":[115,166,171],"systems,":[116],"which":[117],"was":[118],"recently":[119],"introduced":[120],"in":[121,154],"field":[123],"control.":[125],"Similarly,":[126],"phase-type":[135],"multiplier,":[142],"off-diagonal":[145],"meaningfully":[152],"instructive":[153],"search":[156],"for":[157,161],"valid":[159],"establishing":[162],"robust":[163],"closed-loop":[164],"stability,":[165],"cover":[167],"well-known":[169],"small-gain":[170],"recent":[173],"small-phase":[174],"theorems.":[175]},"counts_by_year":[],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-08-05T00:00:00"}