{"id":"https://openalex.org/W3214310669","doi":"https://doi.org/10.1109/tac.2021.3126617","title":"System Monotonicity and Subspace Tracking: A Geometric Perspective of the Frisch\u2013Shapiro Scheme","display_name":"System Monotonicity and Subspace Tracking: A Geometric Perspective of the Frisch\u2013Shapiro Scheme","publication_year":2021,"publication_date":"2021-11-10","ids":{"openalex":"https://openalex.org/W3214310669","doi":"https://doi.org/10.1109/tac.2021.3126617","mag":"3214310669"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2021.3126617","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3126617","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/A5025654724","display_name":"Di Zhao","orcid":"https://orcid.org/0000-0003-2508-9163"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Di Zhao","raw_affiliation_strings":["Department of Control Science and Engineering and Shanghai Institute of Intelligent Science and Technology, Tongji University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0003-2508-9163","affiliations":[{"raw_affiliation_string":"Department of Control Science and Engineering and Shanghai Institute of Intelligent Science and Technology, Tongji University, Shanghai, China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023235121","display_name":"Sei Zhen Khong","orcid":"https://orcid.org/0000-0003-4735-5872"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sei Zhen Khong","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-4735-5872","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5065168162","display_name":"Li Qiu","orcid":"https://orcid.org/0000-0001-8218-9940"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Li Qiu","raw_affiliation_strings":["Department of Electronic and Computer Engineering, University of Science and Technology, Kowloon, Hong Kong, China"],"raw_orcid":"https://orcid.org/0000-0001-8218-9940","affiliations":[{"raw_affiliation_string":"Department of Electronic and Computer Engineering, University of Science and Technology, Kowloon, Hong Kong, China","institution_ids":["https://openalex.org/I200769079"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025654724"],"corresponding_institution_ids":["https://openalex.org/I116953780"],"apc_list":null,"apc_paid":null,"fwci":0.2775,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.56523772,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"67","issue":"11","first_page":"5872","last_page":"5884"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9973999857902527,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9973999857902527,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11236","display_name":"Control Systems and Identification","score":0.9968000054359436,"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/orthant","display_name":"Orthant","score":0.9293560981750488},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.779321551322937},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.652839720249176},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.5871291160583496},{"id":"https://openalex.org/keywords/converse","display_name":"Converse","score":0.5219299793243408},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.48151645064353943},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.45133477449417114},{"id":"https://openalex.org/keywords/diagonal-matrix","display_name":"Diagonal matrix","score":0.4436517357826233},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.44287532567977905},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.43945860862731934},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42455506324768066},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39596280455589294},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37333011627197266},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21462053060531616}],"concepts":[{"id":"https://openalex.org/C2780016784","wikidata":"https://www.wikidata.org/wiki/Q2714507","display_name":"Orthant","level":2,"score":0.9293560981750488},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.779321551322937},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.652839720249176},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5871291160583496},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.5219299793243408},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.48151645064353943},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.45133477449417114},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.4436517357826233},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.44287532567977905},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.43945860862731934},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42455506324768066},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39596280455589294},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37333011627197266},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21462053060531616},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tac.2021.3126617","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3126617","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"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-116781","is_oa":false,"landing_page_url":"http://www.scopus.com/record/display.url?eid=2-s2.0-85140594820&origin=inward","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:repository.ust.hk:1783.1-116781","is_oa":false,"landing_page_url":"http://repository.ust.hk/ir/Record/1783.1-116781","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4403542416","display_name":null,"funder_award_id":"62103303","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W68376499","https://openalex.org/W314209163","https://openalex.org/W1492478997","https://openalex.org/W1588998206","https://openalex.org/W1729590385","https://openalex.org/W1736530648","https://openalex.org/W1851248039","https://openalex.org/W1968135884","https://openalex.org/W1968890997","https://openalex.org/W1975214626","https://openalex.org/W1985782993","https://openalex.org/W2019854158","https://openalex.org/W2038082357","https://openalex.org/W2039726930","https://openalex.org/W2074860140","https://openalex.org/W2084587978","https://openalex.org/W2093038430","https://openalex.org/W2107396783","https://openalex.org/W2133487567","https://openalex.org/W2147326597","https://openalex.org/W2147741970","https://openalex.org/W2153030835","https://openalex.org/W2208136017","https://openalex.org/W2314496443","https://openalex.org/W2343119924","https://openalex.org/W2962976446","https://openalex.org/W2964144599","https://openalex.org/W3011364382","https://openalex.org/W4211118645","https://openalex.org/W4211137119","https://openalex.org/W4211232706","https://openalex.org/W4229706427","https://openalex.org/W4235143360","https://openalex.org/W4252445590","https://openalex.org/W4253168234","https://openalex.org/W4295016751","https://openalex.org/W4298387008","https://openalex.org/W4299821505","https://openalex.org/W6730360565"],"related_works":["https://openalex.org/W2320116587","https://openalex.org/W2788348908","https://openalex.org/W1651216127","https://openalex.org/W2356639438","https://openalex.org/W2037945980","https://openalex.org/W2064847051","https://openalex.org/W2081887375","https://openalex.org/W3122917064","https://openalex.org/W2034108705","https://openalex.org/W2084917546"],"abstract_inverted_index":{"The":[0,85],"Shapiro":[1,30,45],"scheme,":[2,9,26],"together":[3],"with":[4],"the":[5,29,44,51,55,63,101,124],"closely":[6],"related":[7],"Frisch\u2013Kalman":[8],"has":[10],"been":[11],"an":[12],"important":[13,67],"approach":[14],"to":[15,43,50,127],"system":[16],"identification":[17],"and":[18,35,47,75,106,115,131],"statistical":[19],"analysis.":[20],"A":[21],"longstanding":[22],"result":[23,86,103,126],"on":[24],"this":[25],"known":[27],"as":[28,90],"theorem,":[31],"is":[32],"both":[33],"informative":[34],"significant.":[36],"This":[37],"article":[38],"imparts":[39],"a":[40,70,91],"geometric":[41],"understanding":[42],"theorem":[46],"generalizes":[48],"it":[49],"asymmetric":[52],"setting":[53],"using":[54],"notion":[56],"of":[57,69,77,100,110],"cone-invariance.":[58],"In":[59],"particular,":[60],"we":[61,96],"establish":[62],"equivalence":[64],"between":[65],"two":[66,98],"properties":[68],"real-valued":[71],"square":[72],"matrix\u2014irreducible":[73],"orthant-invariance":[74],"simplicity":[76],"its":[78],"dominant":[79],"eigenvalue":[80],"under":[81],"arbitrary":[82],"diagonal":[83],"perturbations.":[84],"can":[87],"be":[88],"regarded":[89],"converse":[92],"Perron\u2013Frobenius":[93],"theorem.":[94],"Furthermore,":[95],"investigate":[97],"applications":[99],"proposed":[102],"in":[104],"systems":[105,114],"control,":[107],"namely,":[108],"characterization":[109],"irreducibly":[111],"orthant-monotone":[112],"nonlinear":[113],"subspace":[116],"tracking":[117],"via":[118],"decentralized":[119],"control.":[120],"We":[121],"also":[122],"extend":[123],"established":[125],"accommodating":[128],"polyhedral":[129],"cones":[130],"obtain":[132],"several":[133],"insights.":[134]},"counts_by_year":[{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}