{"id":"https://openalex.org/W2167075315","doi":"https://doi.org/10.1137/s036301290036851x","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":"2001-01-01","ids":{"openalex":"https://openalex.org/W2167075315","doi":"https://doi.org/10.1137/s036301290036851x","mag":"2167075315"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/s036301290036851x","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://eprints.soton.ac.uk/262216/1/SIAMRiccati.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045235248","display_name":"Harry L. Trentelman","orcid":"https://orcid.org/0000-0001-9463-8651"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"H. L. Trentelman","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5089562946","display_name":"Paolo Rapisarda","orcid":"https://orcid.org/0000-0001-9682-8977"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. Rapisarda","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":21,"citation_normalized_percentile":{"value":0.804122,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":85,"max":86},"biblio":{"volume":"40","issue":"3","first_page":"969","last_page":"991"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9996,"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":0.9996,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9989,"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"}},{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9984,"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/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.66440487},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.6178232},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5482063}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8758249},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.66440487},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.6178232},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.6138308},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.567957},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.55783045},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5482063},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.5460352},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5371357},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.5350353},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.47535536},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46261695},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.4314401},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.41746026},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32597262},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.32369924},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.16819614},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.13837367},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/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},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/s036301290036851x","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://eprints.soton.ac.uk/262216/1/SIAMRiccati.pdf","pdf_url":"https://eprints.soton.ac.uk/262216/1/SIAMRiccati.pdf","source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":["University of Southampton"],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false},{"is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/f4741ff3-1d97-4fef-bb80-b353bc9a3427","pdf_url":"https://research.rug.nl/files/14409099/2001SIAMJContOptimTrentelman.pdf","source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":["Royal Netherlands Academy of Arts and Sciences"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://pure.rug.nl/ws/files/14409099/2001SIAMJContOptimTrentelman.pdf","pdf_url":"https://pure.rug.nl/ws/files/14409099/2001SIAMJContOptimTrentelman.pdf","source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":["University of Groningen"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://eprints.soton.ac.uk/262216/1/SIAMRiccati.pdf","pdf_url":"https://eprints.soton.ac.uk/262216/1/SIAMRiccati.pdf","source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":["University of Southampton"],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":26,"referenced_works":["https://openalex.org/W1498158401","https://openalex.org/W1521555655","https://openalex.org/W1552133866","https://openalex.org/W1972987503","https://openalex.org/W1977481407","https://openalex.org/W197984925","https://openalex.org/W2002357820","https://openalex.org/W2017076495","https://openalex.org/W2037612300","https://openalex.org/W2038724174","https://openalex.org/W2063986193","https://openalex.org/W2077169642","https://openalex.org/W2095878749","https://openalex.org/W2136470155","https://openalex.org/W2139281846","https://openalex.org/W2140883909","https://openalex.org/W2141055453","https://openalex.org/W2146560209","https://openalex.org/W2149811200","https://openalex.org/W2166286857","https://openalex.org/W2171837338","https://openalex.org/W2176175198","https://openalex.org/W2177207193","https://openalex.org/W2755764480","https://openalex.org/W2798813531","https://openalex.org/W4212995568"],"related_works":["https://openalex.org/W3144661763","https://openalex.org/W2334216590","https://openalex.org/W2110484439","https://openalex.org/W2107449083","https://openalex.org/W2096797590","https://openalex.org/W2093124749","https://openalex.org/W2076795936","https://openalex.org/W2076152063","https://openalex.org/W2073418153","https://openalex.org/W2036475854"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,34,56,66,71,89,92,96,101],"existence":[3,35],"of":[4,10,27,36,65,70,83,91,95,103],"positive":[5],"and":[6,30],"negative":[7],"semidefinite":[8],"solutions":[9,38,64,94],"algebraic":[11],"Riccati":[12],"equations":[13],"(ARE)":[14],"corresponding":[15],"to":[16],"linear":[17],"quadratic":[18],"problems":[19],"with":[20,55,75],"an":[21],"indefinite":[22],"cost":[23],"functional.":[24],"The":[25],"formulation":[26],"reasonable":[28],"necessary":[29],"sufficient":[31],"conditions":[32],"for":[33],"such":[37],"is":[39,47],"a":[40,81],"long-standing":[41],"open":[42],"problem.":[43],"A":[44],"central":[45],"role":[46],"played":[48],"by":[49,100],"certain":[50],"two-variable":[51,77],"polynomial":[52,78],"matrices":[53,73],"associated":[54,74],"ARE.":[57],"Our":[58],"main":[59],"result":[60],"characterizes":[61],"all":[62],"unmixed":[63],"ARE":[67,97],"in":[68],"terms":[69],"Pick":[72,105],"these":[76],"matrices.":[79,106],"As":[80],"corollary":[82],"this":[84],"result,":[85],"we":[86],"find":[87],"that":[88],"signatures":[90,102],"extremal":[93],"are":[98],"determined":[99],"particular":[104]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2167075315","counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-04-21T06:05:53.106609","created_date":"2016-06-24"}