{"id":"https://openalex.org/W4246930529","doi":"https://doi.org/10.23919/ecc.2001.7076017","title":"Pick matrix conditions for sign-definite solutions of the algebraic Riccati equation","display_name":"Pick matrix conditions for sign-definite solutions of the algebraic Riccati equation","publication_year":2001,"publication_date":"2001-09-01","ids":{"openalex":"https://openalex.org/W4246930529","doi":"https://doi.org/10.23919/ecc.2001.7076017"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.2001.7076017","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2001.7076017","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2001 European Control Conference (ECC)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5045235248","display_name":"Harry L. Trentelman","orcid":"https://orcid.org/0000-0001-9463-8651"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"H.L. Trentelman","raw_affiliation_strings":["Research Institute for Mathematics and Computer Science, P.O. Box 800, 9700 AV Groningen, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Institute for Mathematics and Computer Science, P.O. Box 800, 9700 AV Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089562946","display_name":"Paolo Rapisarda","orcid":"https://orcid.org/0000-0001-9682-8977"},"institutions":[{"id":"https://openalex.org/I34352273","display_name":"Maastricht University","ror":"https://ror.org/02jz4aj89","country_code":"NL","type":"education","lineage":["https://openalex.org/I34352273"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"P. Rapisarda","raw_affiliation_strings":["Department of Mathematics, University of Maastricht, P.O. Box 616, 6200 MD Maastricht, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Maastricht, P.O. Box 616, 6200 MD Maastricht, The Netherlands","institution_ids":["https://openalex.org/I34352273"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.31586336,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"849","last_page":"853"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9961000084877014,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9961000084877014,"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/T10690","display_name":"Vibration Control and Rheological Fluids","score":0.9598000049591064,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9589999914169312,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.7989717721939087},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7803999185562134},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.6654789447784424},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.631198525428772},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.616470992565155},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.5885623693466187},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5691762566566467},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5562856197357178},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5388360619544983},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.5124369263648987},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.48360195755958557},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.43451425433158875},{"id":"https://openalex.org/keywords/matrix-difference-equation","display_name":"Matrix difference equation","score":0.41676095128059387},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4161284565925598},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3544332981109619},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32263436913490295},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.19545143842697144},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.18850845098495483},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.10620057582855225},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.07635769248008728}],"concepts":[{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.7989717721939087},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7803999185562134},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.6654789447784424},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.631198525428772},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.616470992565155},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.5885623693466187},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5691762566566467},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5562856197357178},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5388360619544983},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.5124369263648987},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.48360195755958557},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43451425433158875},{"id":"https://openalex.org/C47285271","wikidata":"https://www.wikidata.org/wiki/Q6787869","display_name":"Matrix difference equation","level":4,"score":0.41676095128059387},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4161284565925598},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3544332981109619},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32263436913490295},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.19545143842697144},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.18850845098495483},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.10620057582855225},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.07635769248008728},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/ecc.2001.7076017","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2001.7076017","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2001 European Control Conference (ECC)","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":0,"referenced_works":[],"related_works":["https://openalex.org/W2547959172","https://openalex.org/W2018296362","https://openalex.org/W2727200542","https://openalex.org/W2005019312","https://openalex.org/W2804494800","https://openalex.org/W2997206142","https://openalex.org/W2097622270","https://openalex.org/W1561579480","https://openalex.org/W197349956","https://openalex.org/W2114783212"],"abstract_inverted_index":{"Necessary":[0],"and":[1,9],"sufficient":[2],"conditions":[3],"for":[4,62],"the":[5,34,73,77,82,94],"existence":[6],"of":[7,13,54,56,76,81],"positive":[8,63],"negative":[10],"semidefinite":[11],"solutions":[12,75],"algebraic":[14],"Riccati":[15],"equations":[16],"(AREs)":[17],"corresponding":[18],"to":[19,46],"linear":[20],"quadratic":[21],"problems":[22],"with":[23,93],"an":[24,51],"indefinite":[25],"cost":[26],"functional":[27],"are":[28],"formulated.":[29],"The":[30,65],"tests":[31],"known":[32],"from":[33],"literature":[35],"cannot":[36],"be":[37,60],"efficiently":[38],"carried":[39],"out,":[40],"either":[41],"because":[42,50],"they":[43],"apply":[44],"only":[45],"special":[47],"cases,":[48],"or":[49],"infinite":[52],"number":[53],"matrices":[55,85,91],"unbounded":[57],"dimension":[58],"should":[59],"checked":[61],"semidefiniteness.":[64],"results":[66],"presented":[67],"in":[68,79],"this":[69],"paper,":[70],"instead,":[71],"characterize":[72],"extremal":[74],"ARE":[78],"terms":[80],"finite":[83],"Pick":[84],"induced":[86],"by":[87],"certain":[88],"two-variable":[89],"polynomial":[90],"associated":[92],"equation.":[95]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}