{"id":"https://openalex.org/W2064463660","doi":"https://doi.org/10.1109/cdc.2011.6161375","title":"Necessary and Sufficient Conditions for Stabilizability subject to Quadratic Invariance","display_name":"Necessary and Sufficient Conditions for Stabilizability subject to Quadratic Invariance","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2064463660","doi":"https://doi.org/10.1109/cdc.2011.6161375","mag":"2064463660"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2011.6161375","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6161375","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European 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/A5090576506","display_name":"\u015eerban Sab\u0103u","orcid":"https://orcid.org/0000-0001-9999-6757"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Serban Sabau","raw_affiliation_strings":["Electrical and Computer Engineering Department, University of Maryland College Park, College Park, MD, USA","Electrical and Computer Engineering Dept., Univ. of Maryland College Park, 20742-3285, USA"],"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Department, University of Maryland College Park, College Park, MD, USA","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"Electrical and Computer Engineering Dept., Univ. of Maryland College Park, 20742-3285, USA","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065643877","display_name":"Nuno C. Martins","orcid":"https://orcid.org/0000-0003-2083-8102"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nuno C. Martins","raw_affiliation_strings":["Faculty of the Electrical and Computer Engineering Department and the Institute for Systems Research, University of Maryland, College Park, MD, USA","Faculty of the Electrical and Computer Engineering Dept. and the Institute for Systems Research, University of Maryland, College Park, 20742-3285, USA"],"affiliations":[{"raw_affiliation_string":"Faculty of the Electrical and Computer Engineering Department and the Institute for Systems Research, University of Maryland, College Park, MD, USA","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"Faculty of the Electrical and Computer Engineering Dept. and the Institute for Systems Research, University of Maryland, College Park, 20742-3285, USA","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090576506"],"corresponding_institution_ids":["https://openalex.org/I66946132"],"apc_list":null,"apc_paid":null,"fwci":6.5694,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.96385528,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"34","issue":null,"first_page":"2459","last_page":"2466"},"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":0.9984999895095825,"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":0.9984999895095825,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.998199999332428,"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/T11236","display_name":"Control Systems and Identification","score":0.9940000176429749,"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/parametrization","display_name":"Parametrization (atmospheric modeling)","score":0.6552504897117615},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.610643744468689},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5672693252563477},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5315389633178711},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.5305322408676147},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5209727883338928},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5075060725212097},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.465550035238266},{"id":"https://openalex.org/keywords/coprime-integers","display_name":"Coprime integers","score":0.4502604603767395},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44604387879371643},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.42905882000923157},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.42894551157951355},{"id":"https://openalex.org/keywords/quadratic-growth","display_name":"Quadratic growth","score":0.4184281527996063},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41446182131767273},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4126235246658325},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23664045333862305},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2124043107032776},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1007021963596344}],"concepts":[{"id":"https://openalex.org/C202887219","wikidata":"https://www.wikidata.org/wiki/Q3895221","display_name":"Parametrization (atmospheric modeling)","level":3,"score":0.6552504897117615},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.610643744468689},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5672693252563477},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5315389633178711},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5305322408676147},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5209727883338928},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5075060725212097},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.465550035238266},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.4502604603767395},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44604387879371643},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.42905882000923157},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.42894551157951355},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.4184281527996063},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41446182131767273},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4126235246658325},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23664045333862305},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2124043107032776},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1007021963596344},{"id":"https://openalex.org/C74902906","wikidata":"https://www.wikidata.org/wiki/Q1190858","display_name":"Radiative transfer","level":2,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","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},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2011.6161375","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6161375","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European 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":27,"referenced_works":["https://openalex.org/W73711222","https://openalex.org/W163082002","https://openalex.org/W1490746760","https://openalex.org/W1500134124","https://openalex.org/W1514337951","https://openalex.org/W1678129351","https://openalex.org/W1821801801","https://openalex.org/W1868559974","https://openalex.org/W1997935209","https://openalex.org/W2001678265","https://openalex.org/W2010194068","https://openalex.org/W2065313971","https://openalex.org/W2069525910","https://openalex.org/W2086742230","https://openalex.org/W2113789941","https://openalex.org/W2114044578","https://openalex.org/W2118152952","https://openalex.org/W2119052813","https://openalex.org/W2144784103","https://openalex.org/W2150949062","https://openalex.org/W2161237006","https://openalex.org/W2165894964","https://openalex.org/W2166411884","https://openalex.org/W2168209480","https://openalex.org/W2178161518","https://openalex.org/W3195133498","https://openalex.org/W6682033788"],"related_works":["https://openalex.org/W2084086280","https://openalex.org/W2027198738","https://openalex.org/W2397767885","https://openalex.org/W2062514649","https://openalex.org/W2153421756","https://openalex.org/W2054489697","https://openalex.org/W2077818434","https://openalex.org/W2361081803","https://openalex.org/W2083114070","https://openalex.org/W2928558501"],"abstract_inverted_index":{"In":[0],"this":[1,106],"paper":[2,175],"we":[3],"deal":[4],"with":[5,65,188,213],"the":[6,32,54,60,68,84,89,93,102,114,126,141,149,166,192,203,211,223,240,243,255,262,268],"problem":[7],"of":[8,34,83,202,205,210,225,242,245,270],"stabilizing":[9,36,145,248],"linear,":[10],"time-invariant":[11],"plants":[12],"using":[13,120],"feedback":[14],"control":[15],"configurations":[16],"that":[17,26,38,88,143,147,222],"are":[18,62,170,198,260],"subject":[19],"to":[20,67,77,164,185,231,265,277],"sparsity":[21,42,56,90,151,194,215],"constraints.":[22],"Recent":[23],"results":[24,86],"show":[25,221],"given":[27,41,193],"a":[28,45,72,154,162,183,189,206,227,278],"strongly":[29],"stabilizable":[30,187],"plant,":[31,69],"class":[33],"all":[35,246,271],"controllers":[37,249],"satisfy":[39],"certain":[40,218,279],"constraints":[43,57,91,100,152,216,253,259],"admits":[44],"convex":[46,73,99],"representation":[47,74],"via":[48],"Zames's":[49],"Q-parametrization.":[50],"More":[51],"precisely,":[52],"if":[53],"pre-specified":[55],"imposed":[58,150],"on":[59,92,101,140,217,254],"controller":[61,94,111,146,163,190],"quadratically":[63],"invariant":[64],"respect":[66],"then":[70],"such":[71,161,182,226],"is":[75,87,153,229],"guaranteed":[76],"exist.":[78],"The":[79],"most":[80],"useful":[81],"feature":[82],"aforementioned":[85,167],"can":[95],"be":[96,186],"recast":[97],"as":[98],"Q-parameter,":[103],"which":[104],"makes":[105],"approach":[107],"suitable":[108],"for":[109,160,181,261],"optimal":[110,129],"design":[112,158],"(in":[113],"\u210b":[115,130],"<sup":[116,131],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[117,132],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[118,133],"sense)":[119],"numerical":[121],"tools":[122],"readily":[123],"available":[124],"from":[125],"classical,":[127],"centralized":[128],"synthesis.":[134],"All":[135],"these":[136],"procedures":[137,159],"rely":[138],"crucially":[139],"fact":[142],"some":[144],"verifies":[148],"priori":[155],"known,":[156],"while":[157],"initialize":[165],"optimization":[168],"schemes":[169],"not":[171],"yet":[172],"available.":[173],"This":[174],"provides":[176],"necessary":[177],"and":[178],"sufficient":[179],"conditions":[180,197],"plant":[184,212],"having":[191],"pattern.":[195],"These":[196,258],"formulated":[199],"in":[200,267],"terms":[201],"existence":[204],"doubly":[207],"coprime":[208],"factorization":[209,228],"additional":[214,252],"factors.":[219],"We":[220,237],"computation":[224],"equivalent":[230],"solving":[232],"an":[233],"exact":[234],"model-matching":[235],"problem.":[236],"also":[238],"give":[239],"parametrization":[241],"set":[244,269],"decentralized":[247],"by":[250],"imposing":[251],"Youla":[256,263],"parameter.":[257],"parameter":[264],"lie":[266],"stable":[272],"transfer":[273],"function":[274],"matrices":[275],"belonging":[276],"linear":[280],"subspace.":[281]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
