{"id":"https://openalex.org/W2148743793","doi":"https://doi.org/10.1109/cdc.2004.1428956","title":"Computing optimal fixed order H//sub/spl infin//-synthesis values by matrix sum of squares relaxations","display_name":"Computing optimal fixed order H//sub/spl infin//-synthesis values by matrix sum of squares relaxations","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2148743793","doi":"https://doi.org/10.1109/cdc.2004.1428956","mag":"2148743793"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2004.1428956","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2004.1428956","pdf_url":null,"source":{"id":"https://openalex.org/S4363608267","display_name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","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/A5048740385","display_name":"C.W.J. Hol","orcid":null},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"C. Hol","raw_affiliation_strings":["Delft Center of Systems and Control, Delft University of Technnology, Delft, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Delft Center of Systems and Control, Delft University of Technnology, Delft, Netherlands","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035889063","display_name":"Carsten W. Scherer","orcid":"https://orcid.org/0000-0001-8856-2697"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"C. Scherer","raw_affiliation_strings":["Delft Center of Systems and Control, Delft University of Technnology, Delft, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Delft Center of Systems and Control, Delft University of Technnology, Delft, Netherlands","institution_ids":["https://openalex.org/I98358874"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I98358874"],"apc_list":null,"apc_paid":null,"fwci":5.7423,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.96437286,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"3147","last_page":"3153"},"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":0.9997000098228455,"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":0.9997000098228455,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9976000189781189,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9936000108718872,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6625664234161377},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5786076784133911},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.5217952728271484},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4684607684612274},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4438452422618866},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43361395597457886},{"id":"https://openalex.org/keywords/robust-control","display_name":"Robust control","score":0.42310580611228943},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.41848570108413696},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4157503843307495},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34505224227905273},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3386322557926178},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33436718583106995},{"id":"https://openalex.org/keywords/control-system","display_name":"Control system","score":0.12667307257652283},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09068799018859863}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6625664234161377},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5786076784133911},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.5217952728271484},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4684607684612274},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4438452422618866},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43361395597457886},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.42310580611228943},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41848570108413696},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4157503843307495},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34505224227905273},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3386322557926178},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33436718583106995},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.12667307257652283},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09068799018859863},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2004.1428956","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2004.1428956","pdf_url":null,"source":{"id":"https://openalex.org/S4363608267","display_name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1495608639","https://openalex.org/W1513515943","https://openalex.org/W1516549908","https://openalex.org/W1519993568","https://openalex.org/W1544933314","https://openalex.org/W1967344706","https://openalex.org/W1967969202","https://openalex.org/W1996715315","https://openalex.org/W2007784570","https://openalex.org/W2008829493","https://openalex.org/W2015071752","https://openalex.org/W2060583532","https://openalex.org/W2075309787","https://openalex.org/W2082483338","https://openalex.org/W2096140334","https://openalex.org/W2125087034","https://openalex.org/W2133404041","https://openalex.org/W2136619318","https://openalex.org/W2164628203","https://openalex.org/W2472569296","https://openalex.org/W4236486142","https://openalex.org/W4255442211","https://openalex.org/W6682423585","https://openalex.org/W6818080280"],"related_works":["https://openalex.org/W1529675490","https://openalex.org/W2774230986","https://openalex.org/W2049671005","https://openalex.org/W2041766398","https://openalex.org/W1585146120","https://openalex.org/W1507089487","https://openalex.org/W2104028924","https://openalex.org/W2348130481","https://openalex.org/W2164932890","https://openalex.org/W2131905798"],"abstract_inverted_index":{"The":[0,201],"computation":[1,51],"of":[2,44,52,61,112,173,197,214,218,226,235,239],"optimal":[3,36,182],"H":[4,184,221],"<sub":[5,185,222],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[6,186,223],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u221e</sub>":[7,187,224],"controllers":[8],"with":[9,70,103,123,231],"a":[10,110,119,157,219,232],"prescribed":[11],"order":[12,115],"is":[13,21,203],"important":[14],"for":[15,49,176],"their":[16],"real-time":[17],"implementation.":[18],"This":[19],"problem":[20,117,122],"well-known":[22],"to":[23,109,147,168,205,211],"be":[24],"non-convex,":[25],"and":[26,160,210],"only":[27,191],"algorithms":[28],"that":[29,58,101],"compute":[30],"upper":[31],"bounds":[32,179],"on":[33,80,153,163,180],"the":[34,42,50,59,62,71,77,81,99,104,113,124,134,139,164,181,195,198,212,236],"global":[35],"value":[37],"are":[38],"known.":[39],"We":[40,87,143],"consider":[41],"applicability":[43],"matrixvalued":[45],"sum-of-squares":[46],"(sos)":[47],"techniques":[48],"lower":[53,178],"bounds.":[54],"First":[55],"we":[56,75,96,131],"show":[57],"size":[60,190],"Linear":[63],"Matrix":[64],"Inequality":[65],"(LMI)":[66],"relaxations":[67,175],"grow":[68,102,192],"exponentially":[69],"state":[72,105],"dimension":[73,196],"if":[74],"apply":[76],"sos-technique":[78],"directly":[79],"bounded-real":[82],"lemma":[83],"bilinear":[84],"matrix":[85,155],"inequality.":[86],"overcome":[88],"this":[89],"deficiency":[90],"by":[91,137],"two-fold":[92],"sequential":[93],"dualization:":[94],"first":[95],"dualize":[97,132],"in":[98,133,194],"variables":[100,126,136],"dimension,":[106],"which":[107],"leads":[108],"re-formulation":[111],"fixed":[114],"synthesis":[116],"into":[118],"robust":[120,140,149],"analysis":[121],"controller":[125,135,216],"as":[127],"parametric":[128],"uncertainty.":[129],"Second":[130],"relaxing":[138],"LMI":[141,150,174],"problem.":[142],"present":[144],"two":[145,215],"approaches":[146],"solve":[148],"problems":[151],"based":[152,162],"sos":[154],"decompositions,":[156],"direct":[158],"approach":[159],"one":[161],"S-procedure.":[165],"Both":[166],"lead":[167],"an":[169,206,227],"asymptotically":[170],"exact":[171],"family":[172],"computing":[177],"fixed-order":[183],"-norm":[188],"whose":[189],"quadratically":[193],"system":[199],"state.":[200],"method":[202],"applied":[204],"academic":[207],"4th-order":[208],"example":[209],"tuning":[213],"parameters":[217],"4-block":[220],"design":[225],"active":[228],"suspension":[229],"system,":[230],"Mc-Millan":[233],"degree":[234],"weighted":[237],"plant":[238],"27.":[240]},"counts_by_year":[{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
