{"id":"https://openalex.org/W2014883276","doi":"https://doi.org/10.1080/00207170701413843","title":"Structured squaring down and zero assignment","display_name":"Structured squaring down and zero assignment","publication_year":2007,"publication_date":"2007-11-16","ids":{"openalex":"https://openalex.org/W2014883276","doi":"https://doi.org/10.1080/00207170701413843","mag":"2014883276"},"language":"en","primary_location":{"id":"doi:10.1080/00207170701413843","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170701413843","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of 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/A5023395981","display_name":"John Leventides","orcid":"https://orcid.org/0000-0002-4320-3145"},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"J. Leventides","raw_affiliation_strings":["Section of Mathematics and Informatics, Department of Economics , University of Athens , Pezmazoglou 8, Athens, Greece"],"affiliations":[{"raw_affiliation_string":"Section of Mathematics and Informatics, Department of Economics , University of Athens , Pezmazoglou 8, Athens, Greece","institution_ids":["https://openalex.org/I200777214"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048478636","display_name":"N. Karcanias","orcid":"https://orcid.org/0000-0002-1889-6314"},"institutions":[{"id":"https://openalex.org/I180825142","display_name":"City, University of London","ror":"https://ror.org/04489at23","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I180825142"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"N. Karcanias","raw_affiliation_strings":["Control Engineering Centre, School of Engineering & Mathematical Sciences, City University , Northampton Square, London EC1V OHB, UK","Control Engineering Centre, School of Engineering and Mathematical Sciences, City University, Northampton Square London EC1V OHB, UK"],"affiliations":[{"raw_affiliation_string":"Control Engineering Centre, School of Engineering & Mathematical Sciences, City University , Northampton Square, London EC1V OHB, UK","institution_ids":["https://openalex.org/I180825142"]},{"raw_affiliation_string":"Control Engineering Centre, School of Engineering and Mathematical Sciences, City University, Northampton Square London EC1V OHB, UK","institution_ids":["https://openalex.org/I180825142"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5048478636"],"corresponding_institution_ids":["https://openalex.org/I180825142"],"apc_list":null,"apc_paid":null,"fwci":2.0002,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.84676641,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"81","issue":"2","first_page":"294","last_page":"306"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9811999797821045,"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":0.9811999797821045,"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/T10142","display_name":"Formal Methods in Verification","score":0.96670001745224,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9635000228881836,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7750481367111206},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5962157249450684},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5879914164543152},{"id":"https://openalex.org/keywords/zero-set","display_name":"Zero set","score":0.5865621566772461},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.5146363973617554},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4887811839580536},{"id":"https://openalex.org/keywords/feedback-linearization","display_name":"Feedback linearization","score":0.4557381272315979},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.41423481702804565},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.410093754529953},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.38453131914138794},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35291099548339844},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34817448258399963},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2994876205921173},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.18562749028205872},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11624181270599365},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11425206065177917}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7750481367111206},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5962157249450684},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5879914164543152},{"id":"https://openalex.org/C17183583","wikidata":"https://www.wikidata.org/wiki/Q214604","display_name":"Zero set","level":2,"score":0.5865621566772461},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.5146363973617554},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4887811839580536},{"id":"https://openalex.org/C85736874","wikidata":"https://www.wikidata.org/wiki/Q672139","display_name":"Feedback linearization","level":3,"score":0.4557381272315979},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.41423481702804565},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.410093754529953},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.38453131914138794},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35291099548339844},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34817448258399963},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2994876205921173},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.18562749028205872},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11624181270599365},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11425206065177917},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207170701413843","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170701413843","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"},{"id":"pmh:oai:openaccess.city.ac.uk:14047","is_oa":false,"landing_page_url":"https://openaccess.city.ac.uk/view/creators_id/n=2Ekarcanias.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4306401940","display_name":"City Research Online (City University London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I180825142","host_organization_name":"City, University of London","host_organization_lineage":["https://openalex.org/I180825142"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life below water","score":0.4399999976158142,"id":"https://metadata.un.org/sdg/14"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W151017915","https://openalex.org/W391677239","https://openalex.org/W1517540714","https://openalex.org/W1543073047","https://openalex.org/W1543638401","https://openalex.org/W1974526344","https://openalex.org/W1988076923","https://openalex.org/W1988442902","https://openalex.org/W1994858407","https://openalex.org/W1996288653","https://openalex.org/W2001012051","https://openalex.org/W2010474043","https://openalex.org/W2019237924","https://openalex.org/W2020023082","https://openalex.org/W2020395543","https://openalex.org/W2028263451","https://openalex.org/W2043565744","https://openalex.org/W2057238957","https://openalex.org/W2066807205","https://openalex.org/W2076043862","https://openalex.org/W2086742230","https://openalex.org/W2090963365","https://openalex.org/W2121836583","https://openalex.org/W2133379892","https://openalex.org/W2140279008","https://openalex.org/W2147831117","https://openalex.org/W2248984810","https://openalex.org/W2798813531","https://openalex.org/W4243098353","https://openalex.org/W4252637274","https://openalex.org/W4411816191"],"related_works":["https://openalex.org/W1998462347","https://openalex.org/W2349527210","https://openalex.org/W1836713364","https://openalex.org/W2141603307","https://openalex.org/W4300511988","https://openalex.org/W2131265573","https://openalex.org/W2899783744","https://openalex.org/W2317650444","https://openalex.org/W130230158","https://openalex.org/W2913529325"],"abstract_inverted_index":{"The":[0],"problem":[1,63,106],"of":[2,13,37,57,71,77,96,127],"zero":[3],"assignment":[4,88],"by":[5],"squaring":[6,98],"down":[7,99],"is":[8,39,90,102,124,132,140],"considered":[9],"for":[10,28,61,83],"a":[11,35,53,68,133],"system":[12,134],"p-inputs,":[14],"n-outputs":[15],"and":[16,46,74,130,135],"n-states":[17],"(m":[18],">":[19,117],"p),":[20],"where":[21,34,119],"not":[22],"all":[23],"outputs":[24,38,129],"are":[25,49,64],"free":[26],"variables":[27],"design.":[29],"We":[30],"consider":[31],"the":[32,42,47,62,75,78,84,97,105,125,143],"case":[33],"k-subset":[36],"preserved":[40],"in":[41],"new":[43,55,69],"output":[44,85],"set,":[45],"rest":[48],"recombined":[50],"to":[51,92],"produce":[52],"total":[54],"set":[56],"p-outputs.":[58],"New":[59],"invariants":[60],"introduced":[65],"which":[66,139],"include":[67],"class":[70],"fixed":[72,128],"zeros":[73],"methodology":[76],"global":[79],"linearization,":[80],"developed":[81],"originally":[82],"feedback":[86],"pole":[87],"problem,":[89],"applied":[91],"this":[93],"restricted":[94,144],"form":[95],"problem.":[100],"It":[101],"shown":[103],"that":[104],"can":[107],"be":[108],"solved":[109],"generically":[110],"if":[111],"(p":[112],"\u2212":[113,115],"k)(m":[114],"p)":[116,123],"\u03b4*,":[118],"k":[120],"(k":[121],"<":[122],"number":[126],"\u03b4*":[131],"compensation":[136],"scheme":[137],"invariant,":[138],"defined":[141],"as":[142],"Forney":[145],"degree.":[146]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
