{"id":"https://openalex.org/W2208327604","doi":"https://doi.org/10.1109/tac.2012.2191869","title":"Improper &lt;formula formulatype=\"inline\"&gt;&lt;tex Notation=\"TeX\"&gt;${\\cal L}_{\\infty}$&lt;/tex&gt;&lt;/formula&gt; Optimal/Suboptimal Controllers","display_name":"Improper &lt;formula formulatype=\"inline\"&gt;&lt;tex Notation=\"TeX\"&gt;${\\cal L}_{\\infty}$&lt;/tex&gt;&lt;/formula&gt; Optimal/Suboptimal Controllers","publication_year":2012,"publication_date":"2012-03-24","ids":{"openalex":"https://openalex.org/W2208327604","doi":"https://doi.org/10.1109/tac.2012.2191869","mag":"2208327604"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2012.2191869","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2012.2191869","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/A5022706065","display_name":"Debasattam Pal","orcid":"https://orcid.org/0000-0002-4886-3003"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"D. Pal","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004471796","display_name":"Madhu N. Belur","orcid":"https://orcid.org/0000-0002-1942-6293"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"M. N. Belur","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I162827531"],"apc_list":null,"apc_paid":null,"fwci":0.587,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.79698124,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"57","issue":"5","first_page":"1280","last_page":"1285"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9958999752998352,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9945999979972839,"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/controller","display_name":"Controller (irrigation)","score":0.5238261818885803},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42923659086227417},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4233844578266144},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4078778028488159},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37587156891822815},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36573320627212524},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33293619751930237},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30150526762008667}],"concepts":[{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5238261818885803},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42923659086227417},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4233844578266144},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4078778028488159},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37587156891822815},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36573320627212524},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33293619751930237},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30150526762008667},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2012.2191869","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2012.2191869","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:dsapce.library.iitb.ac.in:100/15033","is_oa":false,"landing_page_url":"http://dspace.library.iitb.ac.in/jspui/handle/100/15033","pdf_url":null,"source":{"id":"https://openalex.org/S4306400899","display_name":"DSpace (IIT Bombay)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I162827531","host_organization_name":"Indian Institute of Technology Bombay","host_organization_lineage":["https://openalex.org/I162827531"],"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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1500134124","https://openalex.org/W1976856287","https://openalex.org/W2029456711","https://openalex.org/W2029741856","https://openalex.org/W2066605554","https://openalex.org/W2102712506","https://openalex.org/W2147193288","https://openalex.org/W2171837338","https://openalex.org/W2177207193","https://openalex.org/W4212995568","https://openalex.org/W4242398744"],"related_works":["https://openalex.org/W2188532381","https://openalex.org/W2018505794","https://openalex.org/W2775001251","https://openalex.org/W2933398093","https://openalex.org/W4300527359","https://openalex.org/W2980129445","https://openalex.org/W2910693632","https://openalex.org/W1924480202","https://openalex.org/W4287817389","https://openalex.org/W48459060"],"abstract_inverted_index":{"We":[0,27,133],"considerL\u221e-control":[1],"of":[2,8,116],"MIMO":[3],"systems":[4],"and":[5,45,66,69,76,128],"address":[6],"solvability":[7,75,95],"the":[9,37,41,98,114,117,142],"problem":[10,74],"over":[11],"all":[12],"finite":[13],"dimensional":[14],"LTI":[15],"controllers:":[16],"i.e.,":[17],"controllers":[18,31],"whose":[19],"transfer":[20,109,131,147],"functions":[21],"can":[22,55],"be":[23],"proper":[24,58,127],"or":[25],"improper.":[26],"show":[28],"that":[29,47,89],"improper":[30,53,108,129,146],"are":[32,49],"easily":[33],"dealt":[34],"with":[35,106,125],"using":[36],"behavioral":[38],"approach,":[39],"unlike":[40],"standard":[42],"state-space/transfer-matrix":[43],"methods,":[44],"argue":[46],"there":[48],"cases":[50],"where":[51],"an":[52,100,107,138,145],"controller":[54,102,130],"outperform":[56],"a":[57],"controller.":[59],"In":[60,111],"this":[61,78],"setting,":[62],"we":[63,87],"next":[64],"formulate":[65],"prove":[67],"necessary":[68],"sufficient":[70],"conditions":[71,96],"for":[72,140],"suboptimalL\u221e-control":[73],"relate":[77],"to":[79],"existing":[80],"results":[81,136],"about":[82],"system":[83,120],"invariant":[84],"zeros.":[85],"Further,":[86],"infer":[88],"in":[90],"our":[91],"formulation,":[92],"assuming":[93],"suboptimal":[94],"on":[97],"system,":[99],"optimal":[101],"always":[103],"exists,":[104],"possibly":[105],"function.":[110,148],"other":[112],"words,":[113],"infimumL\u221e-norm":[115],"closed":[118],"loop":[119],"is":[121],"achievable":[122],"when":[123],"dealing":[124],"both":[126],"functions.":[132],"illustrate":[134],"these":[135],"through":[137],"example":[139],"which":[141],"optimalL\u221e-controller":[143],"has":[144]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2016-06-24T00:00:00"}
