{"id":"https://openalex.org/W1518522252","doi":"https://doi.org/10.23919/ecc.1999.7099864","title":"On a rational matrix equation occuring in stochastic control","display_name":"On a rational matrix equation occuring in stochastic control","publication_year":1999,"publication_date":"1999-08-01","ids":{"openalex":"https://openalex.org/W1518522252","doi":"https://doi.org/10.23919/ecc.1999.7099864","mag":"1518522252"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.1999.7099864","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.1999.7099864","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1999 European Control Conference (ECC)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5084460858","display_name":"Tobias Damm","orcid":"https://orcid.org/0000-0002-8550-8174"},"institutions":[{"id":"https://openalex.org/I180437899","display_name":"University of Bremen","ror":"https://ror.org/04ers2y35","country_code":"DE","type":"education","lineage":["https://openalex.org/I180437899"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"T. Damm","raw_affiliation_strings":["Universitat Bremen, Bremen, Bremen, DE","Institute for Dynamical Systems, University of Bremen, 28334 Bremen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universitat Bremen, Bremen, Bremen, DE","institution_ids":["https://openalex.org/I180437899"]},{"raw_affiliation_string":"Institute for Dynamical Systems, University of Bremen, 28334 Bremen, Germany","institution_ids":["https://openalex.org/I180437899"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081067516","display_name":"D. Hinrichsen","orcid":null},"institutions":[{"id":"https://openalex.org/I180437899","display_name":"University of Bremen","ror":"https://ror.org/04ers2y35","country_code":"DE","type":"education","lineage":["https://openalex.org/I180437899"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"D. Hinrichsen","raw_affiliation_strings":["Universitat Bremen, Bremen, Bremen, DE","Institute for Dynamical Systems, University of Bremen, 28334 Bremen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universitat Bremen, Bremen, Bremen, DE","institution_ids":["https://openalex.org/I180437899"]},{"raw_affiliation_string":"Institute for Dynamical Systems, University of Bremen, 28334 Bremen, Germany","institution_ids":["https://openalex.org/I180437899"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I180437899"],"apc_list":null,"apc_paid":null,"fwci":0.3149,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.45410886,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"3458","last_page":"3463"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9986000061035156,"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":0.9986000061035156,"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":0.9984999895095825,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6263868808746338},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.6235611438751221},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.5729619264602661},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5693413019180298},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49724438786506653},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48867157101631165},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.47906216979026794},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4686037302017212},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.45317983627319336},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.4382406771183014},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34095972776412964},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32123827934265137},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21995443105697632},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1886989176273346},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08916041254997253}],"concepts":[{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6263868808746338},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.6235611438751221},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.5729619264602661},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5693413019180298},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49724438786506653},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48867157101631165},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.47906216979026794},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4686037302017212},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.45317983627319336},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.4382406771183014},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34095972776412964},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32123827934265137},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21995443105697632},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1886989176273346},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08916041254997253},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/ecc.1999.7099864","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.1999.7099864","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1999 European Control Conference (ECC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1579485993","https://openalex.org/W2024920306","https://openalex.org/W2051352619","https://openalex.org/W2053327376","https://openalex.org/W2102316513","https://openalex.org/W2145883151"],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2105459831","https://openalex.org/W1546579375","https://openalex.org/W2127238600","https://openalex.org/W2096105566","https://openalex.org/W1563296412","https://openalex.org/W2114791549","https://openalex.org/W16457797","https://openalex.org/W2792258377","https://openalex.org/W1530596433"],"abstract_inverted_index":{"We":[0,45],"regard":[1],"a":[2,47],"general":[3],"class":[4],"of":[5,24,36,53,60],"rational":[6],"matrix":[7],"equations,":[8],"which":[9],"contains":[10],"the":[11,51,58],"continuous":[12],"(CARE)":[13],"and":[14,31,64],"discrete":[15],"(DARE)":[16],"algebraic":[17],"Riccati":[18],"equations":[19,55],"as":[20],"special":[21],"cases.":[22],"Equations":[23],"this":[25],"type":[26],"were":[27,43],"encountered":[28],"in":[29],"[EIIPSG]":[30],"[EHP98]":[32],"where":[33],"H\u221e-typo.":[34],"problems":[35],"disturbance":[37],"attenuation":[38],"for":[39,50],"stochastic":[40],"linear":[41],"systems":[42],"studied.":[44],"develop":[46],"unifying":[48],"framework":[49],"analysis":[52],"these":[54],"based":[56],"on":[57],"theory":[59],"(rcsolvcnt)":[61],"positive":[62],"operators":[63],"show":[65],"that":[66],"they":[67],"can":[68],"be":[69],"solved":[70],"by":[71],"Newton's":[72],"method":[73],"starting":[74],"at":[75],"an":[76],"arbitrary":[77],"stabilizing":[78],"matrix.":[79]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
