{"id":"https://openalex.org/W2040085632","doi":"https://doi.org/10.1016/s0005-1098(01)00230-8","title":"A revised Kleinman algorithm to solve algebraic Riccati equation of singularly perturbed systems","display_name":"A revised Kleinman algorithm to solve algebraic Riccati equation of singularly perturbed systems","publication_year":2002,"publication_date":"2002-03-01","ids":{"openalex":"https://openalex.org/W2040085632","doi":"https://doi.org/10.1016/s0005-1098(01)00230-8","mag":"2040085632"},"language":"en","primary_location":{"id":"doi:10.1016/s0005-1098(01)00230-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0005-1098(01)00230-8","pdf_url":null,"source":{"id":"https://openalex.org/S51360982","display_name":"Automatica","issn_l":"0005-1098","issn":["0005-1098","1873-2836"],"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":"Automatica","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/A5057193482","display_name":"Hiroaki Mukaidani","orcid":"https://orcid.org/0000-0001-6740-7102"},"institutions":[{"id":"https://openalex.org/I57930482","display_name":"Hiroshima City University","ror":"https://ror.org/001et4e78","country_code":"JP","type":"education","lineage":["https://openalex.org/I57930482"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Hiroaki Mukaidani","raw_affiliation_strings":["Faculty of Information Sciences, Hiroshima City University, Asaminami-ku, Hiroshima, 731-3194 Japan","Faculty of Information Sciences, Hiroshima City University, Asaminami-ku, Hiroshima, 731-3194, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Information Sciences, Hiroshima City University, Asaminami-ku, Hiroshima, 731-3194 Japan","institution_ids":["https://openalex.org/I57930482"]},{"raw_affiliation_string":"Faculty of Information Sciences, Hiroshima City University, Asaminami-ku, Hiroshima, 731-3194, Japan","institution_ids":["https://openalex.org/I57930482"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049413017","display_name":"Hua Xu","orcid":"https://orcid.org/0000-0001-5478-6879"},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hua Xu","raw_affiliation_strings":["Graduate School of Business Sciences, The University of Tsukuba, Bunkyou-ku, Tokyo, 112-0012 Japan","Graduate School of Business Sciences, The University of Tsukuba, Bunkyou-ku, Tokyo, 112-0012 Japan#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Business Sciences, The University of Tsukuba, Bunkyou-ku, Tokyo, 112-0012 Japan","institution_ids":["https://openalex.org/I146399215"]},{"raw_affiliation_string":"Graduate School of Business Sciences, The University of Tsukuba, Bunkyou-ku, Tokyo, 112-0012 Japan#TAB#","institution_ids":["https://openalex.org/I146399215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113945718","display_name":"Koichi Mizukami","orcid":null},"institutions":[{"id":"https://openalex.org/I2321252","display_name":"Hiroshima Kokusai Gakuin University","ror":"https://ror.org/00mns7418","country_code":"JP","type":"education","lineage":["https://openalex.org/I2321252"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Koichi Mizukami","raw_affiliation_strings":["Faculty of Engineering, Hiroshima Kokusai Gakuin University, Aki-ku, Hiroshima, 739-0321 Japan","Faculty of Engineering, Hiroshima Kokusai Gakuin University, Aki-ku, Hiroshima, 739-0321 Japan#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Hiroshima Kokusai Gakuin University, Aki-ku, Hiroshima, 739-0321 Japan","institution_ids":["https://openalex.org/I2321252"]},{"raw_affiliation_string":"Faculty of Engineering, Hiroshima Kokusai Gakuin University, Aki-ku, Hiroshima, 739-0321 Japan#TAB#","institution_ids":["https://openalex.org/I2321252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5057193482"],"corresponding_institution_ids":["https://openalex.org/I57930482"],"apc_list":{"value":3500,"currency":"USD","value_usd":3500},"apc_paid":null,"fwci":1.5656,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.81391737,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"38","issue":"3","first_page":"553","last_page":"558"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9990000128746033,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9958000183105469,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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":0.7673754096031189},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.7382799386978149},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.6852381825447083},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6014687418937683},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.5625069737434387},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5611577033996582},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.547265350818634},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5003211498260498},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.45789462327957153},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30829355120658875},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.2496558427810669},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.22023531794548035},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.17753762006759644},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.07145217061042786}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7673754096031189},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.7382799386978149},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.6852381825447083},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6014687418937683},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.5625069737434387},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5611577033996582},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.547265350818634},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5003211498260498},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.45789462327957153},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30829355120658875},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.2496558427810669},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.22023531794548035},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.17753762006759644},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.07145217061042786},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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:10.1016/s0005-1098(01)00230-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0005-1098(01)00230-8","pdf_url":null,"source":{"id":"https://openalex.org/S51360982","display_name":"Automatica","issn_l":"0005-1098","issn":["0005-1098","1873-2836"],"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":"Automatica","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W248453426","https://openalex.org/W1491259464","https://openalex.org/W1515224583","https://openalex.org/W1588998206","https://openalex.org/W1968228551","https://openalex.org/W2027569838","https://openalex.org/W2037025184","https://openalex.org/W2054689585","https://openalex.org/W2059359811","https://openalex.org/W2071933675","https://openalex.org/W2093184664","https://openalex.org/W2099816871","https://openalex.org/W2476615183","https://openalex.org/W2797638056","https://openalex.org/W4243001631","https://openalex.org/W4301272506","https://openalex.org/W4302078450"],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2547959172","https://openalex.org/W2018296362","https://openalex.org/W2727200542","https://openalex.org/W2002357820","https://openalex.org/W197349956","https://openalex.org/W2997206142","https://openalex.org/W2027962246","https://openalex.org/W2116228702","https://openalex.org/W2244442793"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":2}],"updated_date":"2026-05-20T08:49:12.498775","created_date":"2025-10-10T00:00:00"}