{"id":"https://openalex.org/W2125674289","doi":"https://doi.org/10.1109/acc.2008.4586881","title":"Closed form solutions of the Sylvester and the Lyapunov equations - closed form Gramians","display_name":"Closed form solutions of the Sylvester and the Lyapunov equations - closed form Gramians","publication_year":2008,"publication_date":"2008-06-01","ids":{"openalex":"https://openalex.org/W2125674289","doi":"https://doi.org/10.1109/acc.2008.4586881","mag":"2125674289"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2008.4586881","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2008.4586881","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 American Control Conference","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/A5017346265","display_name":"A.S. Hauksd\u00f3ttir","orcid":null},"institutions":[{"id":"https://openalex.org/I165368041","display_name":"University of Iceland","ror":"https://ror.org/01db6h964","country_code":"IS","type":"education","lineage":["https://openalex.org/I165368041"]}],"countries":["IS"],"is_corresponding":false,"raw_author_name":"Anna Soffia Hauksdottir","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Iceland, Reykjavik, Iceland","University of Iceland [Reykjavik]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Iceland, Reykjavik, Iceland","institution_ids":["https://openalex.org/I165368041"]},{"raw_affiliation_string":"University of Iceland [Reykjavik]","institution_ids":["https://openalex.org/I165368041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077220955","display_name":"Sven P. Sigurdsson","orcid":null},"institutions":[{"id":"https://openalex.org/I165368041","display_name":"University of Iceland","ror":"https://ror.org/01db6h964","country_code":"IS","type":"education","lineage":["https://openalex.org/I165368041"]}],"countries":["IS"],"is_corresponding":false,"raw_author_name":"Sven P. Sigurdsson","raw_affiliation_strings":["Department of Computer Science, University of Iceland, Reykjavik, Iceland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Iceland, Reykjavik, Iceland","institution_ids":["https://openalex.org/I165368041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5097485076","display_name":"Sigurour Orn Adalgeirsson","orcid":null},"institutions":[{"id":"https://openalex.org/I165368041","display_name":"University of Iceland","ror":"https://ror.org/01db6h964","country_code":"IS","type":"education","lineage":["https://openalex.org/I165368041"]}],"countries":["IS"],"is_corresponding":false,"raw_author_name":"Sigurour Orn Adalgeirsson","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Iceland, Reykjavik, Iceland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Iceland, Reykjavik, Iceland","institution_ids":["https://openalex.org/I165368041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033206223","display_name":"Helgi Porgilsson","orcid":null},"institutions":[{"id":"https://openalex.org/I165368041","display_name":"University of Iceland","ror":"https://ror.org/01db6h964","country_code":"IS","type":"education","lineage":["https://openalex.org/I165368041"]}],"countries":["IS"],"is_corresponding":false,"raw_author_name":"Helgi Porgilsson","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Iceland, Reykjavik, Iceland","[Dept. of Electrical and Computer Engineering, University of Iceland, Reykjavik, Iceland]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Iceland, Reykjavik, Iceland","institution_ids":["https://openalex.org/I165368041"]},{"raw_affiliation_string":"[Dept. of Electrical and Computer Engineering, University of Iceland, Reykjavik, Iceland]","institution_ids":["https://openalex.org/I165368041"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076257256","display_name":"G\u00edsli Herj\u00f3lfsson","orcid":null},"institutions":[{"id":"https://openalex.org/I165368041","display_name":"University of Iceland","ror":"https://ror.org/01db6h964","country_code":"IS","type":"education","lineage":["https://openalex.org/I165368041"]}],"countries":["IS"],"is_corresponding":false,"raw_author_name":"Gisli Herjolfsson","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Iceland, Reykjavik, Iceland","[Dept. of Electrical and Computer Engineering, University of Iceland, Reykjavik, Iceland]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Iceland, Reykjavik, Iceland","institution_ids":["https://openalex.org/I165368041"]},{"raw_affiliation_string":"[Dept. of Electrical and Computer Engineering, University of Iceland, Reykjavik, Iceland]","institution_ids":["https://openalex.org/I165368041"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I165368041"],"apc_list":null,"apc_paid":null,"fwci":0.3239,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.65551266,"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":"2585","last_page":"2590"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9972000122070312,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9958999752998352,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sylvester-equation","display_name":"Sylvester equation","score":0.7911123037338257},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.7109792232513428},{"id":"https://openalex.org/keywords/closed-form-expression","display_name":"Closed-form expression","score":0.5967613458633423},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5637171268463135},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5586435198783875},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5131738781929016},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5123351812362671},{"id":"https://openalex.org/keywords/sylvesters-law-of-inertia","display_name":"Sylvester's law of inertia","score":0.5006804466247559},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4789995849132538},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.34473830461502075},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3026476502418518},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28431767225265503},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.2603754997253418},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.22102195024490356},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.15194803476333618},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.07694816589355469},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06692975759506226}],"concepts":[{"id":"https://openalex.org/C100468782","wikidata":"https://www.wikidata.org/wiki/Q3730848","display_name":"Sylvester equation","level":3,"score":0.7911123037338257},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.7109792232513428},{"id":"https://openalex.org/C4530962","wikidata":"https://www.wikidata.org/wiki/Q777407","display_name":"Closed-form expression","level":2,"score":0.5967613458633423},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5637171268463135},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5586435198783875},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5131738781929016},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5123351812362671},{"id":"https://openalex.org/C56828936","wikidata":"https://www.wikidata.org/wiki/Q1752621","display_name":"Sylvester's law of inertia","level":4,"score":0.5006804466247559},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4789995849132538},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.34473830461502075},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3026476502418518},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28431767225265503},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.2603754997253418},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.22102195024490356},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.15194803476333618},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.07694816589355469},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06692975759506226},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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},{"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/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2008.4586881","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2008.4586881","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323298","display_name":"H\u00e1sk\u00f3li \u00cdslands","ror":"https://ror.org/01db6h964"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1965854789","https://openalex.org/W1981860330","https://openalex.org/W2013276465","https://openalex.org/W2039700298","https://openalex.org/W2067136705","https://openalex.org/W2074489482","https://openalex.org/W2088748973","https://openalex.org/W2106565812","https://openalex.org/W2124956430","https://openalex.org/W2130727150","https://openalex.org/W2140066476","https://openalex.org/W2143684599","https://openalex.org/W2145214219","https://openalex.org/W2146035727","https://openalex.org/W2154810024","https://openalex.org/W2160835412","https://openalex.org/W4206263661"],"related_works":["https://openalex.org/W1597114477","https://openalex.org/W2087190655","https://openalex.org/W2355051888","https://openalex.org/W2907087892","https://openalex.org/W2502651484","https://openalex.org/W837678188","https://openalex.org/W2125674289","https://openalex.org/W2104785239","https://openalex.org/W2795777210","https://openalex.org/W1545249449"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"closed":[3,22],"form":[4,74],"expressions":[5,69],"of":[6,17,28,32],"linear":[7],"MIMO":[8],"system":[9],"responses":[10],"are":[11,51,70],"used":[12],"to":[13,36],"express":[14],"the":[15,18,37,40,45,48,60,81],"solution":[16,25],"Sylvester":[19],"equation":[20],"in":[21,72],"form.":[23],"The":[24,34,67],"makes":[26],"use":[27],"matrix":[29],"polynomial":[30],"formulations":[31],"etA.":[33],"solutions":[35],"input":[38,46],"and":[39,47,80],"output":[41,49],"Lyapunov":[42],"equations,":[43],"i.e.":[44],"Gramians,":[50],"then":[52],"presented":[53,71],"as":[54],"a":[55,73],"special":[56],"case.":[57],"From":[58],"these":[59],"Hankel":[61],"singular":[62],"values":[63],"can":[64],"be":[65],"computed.":[66],"final":[68],"that":[75],"emphasizes":[76],"efficient":[77],"computational":[78],"implementation":[79],"resulting":[82],"time":[83],"complexity.":[84]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}