{"id":"https://openalex.org/W2148247809","doi":"https://doi.org/10.1109/cdc.2010.5717592","title":"On the continuous-time algebraic Riccati equation and its closed-form solution","display_name":"On the continuous-time algebraic Riccati equation and its closed-form solution","publication_year":2010,"publication_date":"2010-12-01","ids":{"openalex":"https://openalex.org/W2148247809","doi":"https://doi.org/10.1109/cdc.2010.5717592","mag":"2148247809"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2010.5717592","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2010.5717592","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"49th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-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/A5039976676","display_name":"Alejandro J. Rojas","orcid":"https://orcid.org/0000-0002-3867-6909"},"institutions":[{"id":"https://openalex.org/I172787465","display_name":"University of Concepci\u00f3n","ror":"https://ror.org/0460jpj73","country_code":"CL","type":"education","lineage":["https://openalex.org/I172787465"]}],"countries":["CL"],"is_corresponding":true,"raw_author_name":"A.J. Rojas","raw_affiliation_strings":["Departamento de Ingenier\u00eda El\u00e9ctrica, Universidad de Concepci\u00f2n, Chile"],"affiliations":[{"raw_affiliation_string":"Departamento de Ingenier\u00eda El\u00e9ctrica, Universidad de Concepci\u00f2n, Chile","institution_ids":["https://openalex.org/I172787465"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039976676"],"corresponding_institution_ids":["https://openalex.org/I172787465"],"apc_list":null,"apc_paid":null,"fwci":0.2312,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.59254793,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1330","last_page":"1335"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9993000030517578,"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":0.9993000030517578,"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/T10305","display_name":"Power System Optimization and Stability","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9987000226974487,"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/controllability","display_name":"Controllability","score":0.8413790464401245},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.8269787430763245},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.7223918437957764},{"id":"https://openalex.org/keywords/closed-form-expression","display_name":"Closed-form expression","score":0.669952392578125},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.669147789478302},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6620895266532898},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6135956645011902},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5679410696029663},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5390068888664246},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5256672501564026},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.511590301990509},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47472938895225525},{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.412825345993042},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.3540504574775696},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3003975450992584},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.242381751537323},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2395862638950348},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.17643341422080994}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.8413790464401245},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.8269787430763245},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.7223918437957764},{"id":"https://openalex.org/C4530962","wikidata":"https://www.wikidata.org/wiki/Q777407","display_name":"Closed-form expression","level":2,"score":0.669952392578125},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.669147789478302},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6620895266532898},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6135956645011902},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5679410696029663},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5390068888664246},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5256672501564026},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.511590301990509},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47472938895225525},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.412825345993042},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3540504574775696},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3003975450992584},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.242381751537323},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2395862638950348},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.17643341422080994},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/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/cdc.2010.5717592","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2010.5717592","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"49th IEEE Conference on Decision and Control (CDC)","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":23,"referenced_works":["https://openalex.org/W1536997931","https://openalex.org/W1562327279","https://openalex.org/W1600349401","https://openalex.org/W1868559974","https://openalex.org/W1965640670","https://openalex.org/W1976169918","https://openalex.org/W1977532666","https://openalex.org/W1997301031","https://openalex.org/W2041742710","https://openalex.org/W2042106612","https://openalex.org/W2053110557","https://openalex.org/W2065313971","https://openalex.org/W2069863818","https://openalex.org/W2092783757","https://openalex.org/W2114418787","https://openalex.org/W2115653641","https://openalex.org/W2138688253","https://openalex.org/W2146055892","https://openalex.org/W2166735509","https://openalex.org/W2261330695","https://openalex.org/W2482852814","https://openalex.org/W3195133498","https://openalex.org/W4388319978"],"related_works":["https://openalex.org/W1978366146","https://openalex.org/W2152163437","https://openalex.org/W2002790969","https://openalex.org/W2036475854","https://openalex.org/W1991511812","https://openalex.org/W2054667646","https://openalex.org/W2058753964","https://openalex.org/W2325104896","https://openalex.org/W4366829194","https://openalex.org/W2086439940"],"abstract_inverted_index":{"In":[0],"the":[1,10,19,22,61,71,81],"present":[2],"paper":[3],"we":[4,79],"obtain":[5],"a":[6,67],"closed-form":[7,29,68],"solution":[8,30],"for":[9,65,70],"class":[11],"of":[12,21,38,48,60],"continuous-time":[13],"algebraic":[14],"Riccati":[15],"equations":[16],"(CTARE),":[17],"whenever":[18],"eigenvalues":[20],"A":[23],"matrix":[24,75],"are":[25],"distinct.":[26],"The":[27],"obtained":[28],"gives":[31],"insight":[32],"on":[33],"issues":[34],"such":[35],"as":[36],"loss":[37],"controllability":[39],"and":[40,85],"it":[41],"might":[42],"also":[43,56],"prove":[44],"comparable":[45],"in":[46],"terms":[47],"numerical":[49],"precision":[50],"over":[51],"current":[52],"solving":[53],"algorithms.":[54],"We":[55],"consider":[57],"further":[58],"extensions":[59],"main":[62],"result":[63],"including,":[64],"example,":[66],"expression":[69],"optimal":[72],"regulator":[73],"gain":[74],"K.":[76],"Whenever":[77],"possible":[78],"discuss":[80],"connection":[82],"with":[83],"earlier":[84],"established":[86],"results.":[87]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}