{"id":"https://openalex.org/W2088672366","doi":"https://doi.org/10.1109/tac.2011.2179429","title":"A New Approach for Upper Bound Estimations of the Solution of the Continuous Riccati Equation","display_name":"A New Approach for Upper Bound Estimations of the Solution of the Continuous Riccati Equation","publication_year":2011,"publication_date":"2011-12-12","ids":{"openalex":"https://openalex.org/W2088672366","doi":"https://doi.org/10.1109/tac.2011.2179429","mag":"2088672366"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2011.2179429","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2011.2179429","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/A5066660142","display_name":"Chien\u2010Hua Lee","orcid":"https://orcid.org/0000-0003-4389-5062"},"institutions":[{"id":"https://openalex.org/I91951123","display_name":"Cheng Shiu University","ror":"https://ror.org/011bdtx65","country_code":"TW","type":"education","lineage":["https://openalex.org/I91951123"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Chien-Hua Lee","raw_affiliation_strings":["Electrical Engineering Department, Cheng Shiu University, Kaohsiung, Taiwan","Electr. Eng. Dept., Cheng-Shiu Univ., Kaohsiung, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical Engineering Department, Cheng Shiu University, Kaohsiung, Taiwan","institution_ids":["https://openalex.org/I91951123"]},{"raw_affiliation_string":"Electr. Eng. Dept., Cheng-Shiu Univ., Kaohsiung, Taiwan","institution_ids":["https://openalex.org/I91951123"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066660142"],"corresponding_institution_ids":["https://openalex.org/I91951123"],"apc_list":null,"apc_paid":null,"fwci":0.3191,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.61595078,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"57","issue":"8","first_page":"2074","last_page":"2077"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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":0.9995999932289124,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9983000159263611,"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/T11236","display_name":"Control Systems and Identification","score":0.9980000257492065,"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":0.9414131045341492},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.8579888343811035},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6668947339057922},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6642642617225647},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5837368965148926},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.5663026571273804},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5016999244689941},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.4825591444969177},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4626513421535492},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.45195478200912476},{"id":"https://openalex.org/keywords/linear-quadratic-gaussian-control","display_name":"Linear-quadratic-Gaussian control","score":0.4453241229057312},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.31624388694763184},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1763167381286621},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17243081331253052},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.05060696601867676}],"concepts":[{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.9414131045341492},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.8579888343811035},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6668947339057922},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6642642617225647},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5837368965148926},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.5663026571273804},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5016999244689941},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.4825591444969177},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4626513421535492},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.45195478200912476},{"id":"https://openalex.org/C204495892","wikidata":"https://www.wikidata.org/wiki/Q1798304","display_name":"Linear-quadratic-Gaussian control","level":3,"score":0.4453241229057312},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31624388694763184},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1763167381286621},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17243081331253052},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.05060696601867676},{"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},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2011.2179429","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2011.2179429","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1502328174","https://openalex.org/W1509538959","https://openalex.org/W1970257841","https://openalex.org/W1976805692","https://openalex.org/W1982955548","https://openalex.org/W1992363721","https://openalex.org/W1999785019","https://openalex.org/W2002790969","https://openalex.org/W2005604276","https://openalex.org/W2012057157","https://openalex.org/W2020247958","https://openalex.org/W2024075554","https://openalex.org/W2037025184","https://openalex.org/W2039827250","https://openalex.org/W2041833020","https://openalex.org/W2048640336","https://openalex.org/W2055031633","https://openalex.org/W2057471928","https://openalex.org/W2065575594","https://openalex.org/W2067328528","https://openalex.org/W2070000969","https://openalex.org/W2071864082","https://openalex.org/W2084401098","https://openalex.org/W2090493874","https://openalex.org/W2097521761","https://openalex.org/W2113442734","https://openalex.org/W2116877555","https://openalex.org/W2117789350","https://openalex.org/W2126425578","https://openalex.org/W2161971587","https://openalex.org/W2167066687","https://openalex.org/W2170041202","https://openalex.org/W6677027393"],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2018296362","https://openalex.org/W2107449083","https://openalex.org/W2547959172","https://openalex.org/W2726381554","https://openalex.org/W2002357820","https://openalex.org/W1737855854","https://openalex.org/W197349956","https://openalex.org/W2997206142","https://openalex.org/W2804494800"],"abstract_inverted_index":{"By":[0],"utilizing":[1],"some":[2],"linear":[3],"algebraic":[4,19],"techniques,":[5],"a":[6],"new":[7],"approach":[8],"for":[9],"measuring":[10],"upper":[11,26],"bounds":[12,28,40],"of":[13,16],"the":[14,17,36,38],"solution":[15],"continuous":[18],"Riccati":[20],"equation":[21],"(CARE)":[22],"is":[23],"developed.":[24,30],"Two":[25],"matrix":[27],"are":[29,41],"Comparing":[31],"with":[32,55],"those":[33],"appeared":[34],"in":[35],"literature,":[37],"obtained":[39],"less":[42],"restrictive":[43],"or":[44],"more":[45],"concise.":[46],"Therefore,":[47],"they":[48],"can":[49],"be":[50],"applied":[51],"easily":[52],"to":[53],"deal":[54],"control":[56],"problems.":[57]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}