{"id":"https://openalex.org/W1983707746","doi":"https://doi.org/10.1016/s0947-3580(99)70159-7","title":"How to Decompose Semi-definite Discrete-Time Algebraic Riccati Equations","display_name":"How to Decompose Semi-definite Discrete-Time Algebraic Riccati Equations","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W1983707746","doi":"https://doi.org/10.1016/s0947-3580(99)70159-7","mag":"1983707746"},"language":"en","primary_location":{"id":"doi:10.1016/s0947-3580(99)70159-7","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0947-3580(99)70159-7","pdf_url":null,"source":{"id":"https://openalex.org/S21401918","display_name":"European Journal of Control","issn_l":"0947-3580","issn":["0947-3580","1435-5671"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of 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/A5057200465","display_name":"Anders Hansson","orcid":null},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]},{"id":"https://openalex.org/I4210090800","display_name":"Sensors (United States)","ror":"https://ror.org/00b4mz884","country_code":"US","type":"company","lineage":["https://openalex.org/I4210090800"]}],"countries":["SE","US"],"is_corresponding":true,"raw_author_name":"A. Hansson","raw_affiliation_strings":["Department of Signals, Sensors and Systems, Royal Institute of Technology, Stockholm"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Signals, Sensors and Systems, Royal Institute of Technology, Stockholm","institution_ids":["https://openalex.org/I86987016","https://openalex.org/I4210090800"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055947027","display_name":"Per Hagander","orcid":null},"institutions":[{"id":"https://openalex.org/I187531555","display_name":"Lund University","ror":"https://ror.org/012a77v79","country_code":"SE","type":"education","lineage":["https://openalex.org/I187531555"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"P. Hagander","raw_affiliation_strings":["Department of Automatic Control, Lund Institute of Technology, Lund, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Automatic Control, Lund Institute of Technology, Lund, Sweden","institution_ids":["https://openalex.org/I187531555"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5057200465"],"corresponding_institution_ids":["https://openalex.org/I4210090800","https://openalex.org/I86987016"],"apc_list":{"value":2850,"currency":"USD","value_usd":2850},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.08645177,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"5","issue":"2-4","first_page":"245","last_page":"258"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9994000196456909,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9940999746322632,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9843999743461609,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.8512733578681946},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.8308627605438232},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7392044067382812},{"id":"https://openalex.org/keywords/unit-circle","display_name":"Unit circle","score":0.6314367055892944},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.587758481502533},{"id":"https://openalex.org/keywords/constructive-proof","display_name":"Constructive proof","score":0.5665895938873291},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.526459276676178},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49616655707359314},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.4861140251159668},{"id":"https://openalex.org/keywords/algebraic-solution","display_name":"Algebraic solution","score":0.4828665554523468},{"id":"https://openalex.org/keywords/algebraic-function","display_name":"Algebraic function","score":0.46770259737968445},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.466992050409317},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.46379074454307556},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.428725004196167},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2700072228908539},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.2271793782711029},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.21029523015022278},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.18083137273788452},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.14865130186080933},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.13743102550506592},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.1363205909729004},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.12812262773513794},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.12315258383750916},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12214446067810059}],"concepts":[{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.8512733578681946},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.8308627605438232},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7392044067382812},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.6314367055892944},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.587758481502533},{"id":"https://openalex.org/C202854965","wikidata":"https://www.wikidata.org/wiki/Q3044470","display_name":"Constructive proof","level":2,"score":0.5665895938873291},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.526459276676178},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49616655707359314},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.4861140251159668},{"id":"https://openalex.org/C87563608","wikidata":"https://www.wikidata.org/wiki/Q2900186","display_name":"Algebraic solution","level":5,"score":0.4828665554523468},{"id":"https://openalex.org/C148607811","wikidata":"https://www.wikidata.org/wiki/Q746863","display_name":"Algebraic function","level":3,"score":0.46770259737968445},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.466992050409317},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.46379074454307556},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.428725004196167},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2700072228908539},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2271793782711029},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.21029523015022278},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.18083137273788452},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.14865130186080933},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.13743102550506592},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.1363205909729004},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.12812262773513794},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.12315258383750916},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12214446067810059},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"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/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/s0947-3580(99)70159-7","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0947-3580(99)70159-7","pdf_url":null,"source":{"id":"https://openalex.org/S21401918","display_name":"European Journal of Control","issn_l":"0947-3580","issn":["0947-3580","1435-5671"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Control","raw_type":"journal-article"},{"id":"pmh:oai:lup.lub.lu.se:5682a512-0507-4338-9cc1-a265baea979f","is_oa":false,"landing_page_url":"https://lup.lub.lu.se/record/8497057","pdf_url":null,"source":{"id":"https://openalex.org/S4306400536","display_name":"Lund University Publications (Lund University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I187531555","host_organization_name":"Lund University","host_organization_lineage":["https://openalex.org/I187531555"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1435-5671","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W96651244","https://openalex.org/W154292103","https://openalex.org/W197984925","https://openalex.org/W1510461155","https://openalex.org/W1518729342","https://openalex.org/W1600349401","https://openalex.org/W1695940191","https://openalex.org/W1968129340","https://openalex.org/W1975736826","https://openalex.org/W1976825368","https://openalex.org/W1977532666","https://openalex.org/W1987035720","https://openalex.org/W1989480656","https://openalex.org/W1994619423","https://openalex.org/W2017801049","https://openalex.org/W2019864386","https://openalex.org/W2031671752","https://openalex.org/W2032682272","https://openalex.org/W2051438607","https://openalex.org/W2052968934","https://openalex.org/W2065457381","https://openalex.org/W2067395537","https://openalex.org/W2086641306","https://openalex.org/W2091367811","https://openalex.org/W2094429957","https://openalex.org/W2095848239","https://openalex.org/W2097156328","https://openalex.org/W2097327029","https://openalex.org/W2097415784","https://openalex.org/W2102575629","https://openalex.org/W2112878831","https://openalex.org/W2122939489","https://openalex.org/W2129881848","https://openalex.org/W2132123183","https://openalex.org/W2147016807","https://openalex.org/W2154627416","https://openalex.org/W2154662331","https://openalex.org/W2163334725","https://openalex.org/W2171612575","https://openalex.org/W2279598329","https://openalex.org/W2478039428","https://openalex.org/W2531455017","https://openalex.org/W2548131485","https://openalex.org/W2595897327","https://openalex.org/W2621510696","https://openalex.org/W2798813531","https://openalex.org/W3031081200","https://openalex.org/W3035578948","https://openalex.org/W4388319978","https://openalex.org/W6604032560","https://openalex.org/W6635868182","https://openalex.org/W6682000412","https://openalex.org/W6695245463","https://openalex.org/W6778567207","https://openalex.org/W6780383567","https://openalex.org/W7011546097"],"related_works":["https://openalex.org/W16457797","https://openalex.org/W2792258377","https://openalex.org/W2185164249","https://openalex.org/W2124522014","https://openalex.org/W1978366146","https://openalex.org/W2152798517","https://openalex.org/W1514186293","https://openalex.org/W1983707746","https://openalex.org/W2014613514","https://openalex.org/W2408624816"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
