{"id":"https://openalex.org/W2046418407","doi":"https://doi.org/10.1137/080742725","title":"General Matrix Pencil Techniques for Solving Discrete-Time Nonsymmetric Algebraic Riccati Equations","display_name":"General Matrix Pencil Techniques for Solving Discrete-Time Nonsymmetric Algebraic Riccati Equations","publication_year":2009,"publication_date":"2009-11-04","ids":{"openalex":"https://openalex.org/W2046418407","doi":"https://doi.org/10.1137/080742725","mag":"2046418407"},"language":"en","primary_location":{"id":"doi:10.1137/080742725","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080742725","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00429802","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002669063","display_name":"Marc Jungers","orcid":"https://orcid.org/0000-0002-6670-3249"},"institutions":[{"id":"https://openalex.org/I4210110792","display_name":"Centre de Recherche en Automatique de Nancy","ror":"https://ror.org/022r5hc56","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210099203","https://openalex.org/I4210100260","https://openalex.org/I4210110792","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Marc Jungers","raw_affiliation_strings":["CRAN - Centre de Recherche en Automatique de Nancy (Universit\u00e9 Henri Poincar\u00e9, 2 avenue de la for\u00eat de Haye, 54516 Vandoeuvre les Nancy - France)"],"affiliations":[{"raw_affiliation_string":"CRAN - Centre de Recherche en Automatique de Nancy (Universit\u00e9 Henri Poincar\u00e9, 2 avenue de la for\u00eat de Haye, 54516 Vandoeuvre les Nancy - France)","institution_ids":["https://openalex.org/I4210110792","https://openalex.org/I90183372"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003304788","display_name":"Cristian Oar\u00e2","orcid":"https://orcid.org/0000-0001-6972-6182"},"institutions":[{"id":"https://openalex.org/I4210141520","display_name":"Societate Comerciala Pentru Cercetare, Proiectare si Productie de Echipamente si Instalatii de Automatizare (Romania)","ror":"https://ror.org/0581ret63","country_code":"RO","type":"company","lineage":["https://openalex.org/I4210141520"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Cristian Oar\u0103","raw_affiliation_strings":["Faculty of Automatic Control and Computers (Splaiul Independentei 313 Romania - Romania)"],"affiliations":[{"raw_affiliation_string":"Faculty of Automatic Control and Computers (Splaiul Independentei 313 Romania - Romania)","institution_ids":["https://openalex.org/I4210141520"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056037472","display_name":"Hisham Abou\u2010Kandil","orcid":null},"institutions":[{"id":"https://openalex.org/I4210136613","display_name":"Laboratoire des syst\u00e8mes et applications des technologies de l'information et de l'\u00e9nergie","ror":"https://ror.org/03vam5b06","country_code":"FR","type":"facility","lineage":["https://openalex.org/I11559806","https://openalex.org/I124158823","https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210134562","https://openalex.org/I4210136613","https://openalex.org/I4210142324","https://openalex.org/I4210154111"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Hisham Abou-Kandil","raw_affiliation_strings":["SATIE - Syst\u00e8mes et Applications des Technologies de l'Information et de l'Energie (61 av du President Wilson 94235 CACHAN Cedex - France)"],"affiliations":[{"raw_affiliation_string":"SATIE - Syst\u00e8mes et Applications des Technologies de l'Information et de l'Energie (61 av du President Wilson 94235 CACHAN Cedex - France)","institution_ids":["https://openalex.org/I4210136613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088757728","display_name":"R. \u015etefan","orcid":"https://orcid.org/0000-0001-5058-8023"},"institutions":[{"id":"https://openalex.org/I4210141520","display_name":"Societate Comerciala Pentru Cercetare, Proiectare si Productie de Echipamente si Instalatii de Automatizare (Romania)","ror":"https://ror.org/0581ret63","country_code":"RO","type":"company","lineage":["https://openalex.org/I4210141520"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Radu \u015etefan","raw_affiliation_strings":["Faculty of Automatic Control and Computers (Splaiul Independentei 313 Romania - Romania)"],"affiliations":[{"raw_affiliation_string":"Faculty of Automatic Control and Computers (Splaiul Independentei 313 Romania - Romania)","institution_ids":["https://openalex.org/I4210141520"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5002669063"],"corresponding_institution_ids":["https://openalex.org/I4210110792","https://openalex.org/I90183372"],"apc_list":null,"apc_paid":null,"fwci":0.7173,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.71186647,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"31","issue":"3","first_page":"1257","last_page":"1278"},"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9955000281333923,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8468778133392334},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.800734281539917},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.6511573195457458},{"id":"https://openalex.org/keywords/matrix-pencil","display_name":"Matrix pencil","score":0.6282356977462769},{"id":"https://openalex.org/keywords/pencil","display_name":"Pencil (optics)","score":0.6272860765457153},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5628857016563416},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5541107058525085},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5172134637832642},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.4627198576927185},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.45889827609062195},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.356781005859375},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22840014100074768},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.12892794609069824},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.11417779326438904}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8468778133392334},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.800734281539917},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.6511573195457458},{"id":"https://openalex.org/C1576492","wikidata":"https://www.wikidata.org/wiki/Q3739929","display_name":"Matrix pencil","level":3,"score":0.6282356977462769},{"id":"https://openalex.org/C134949993","wikidata":"https://www.wikidata.org/wiki/Q2068617","display_name":"Pencil (optics)","level":2,"score":0.6272860765457153},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5628857016563416},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5541107058525085},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5172134637832642},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.4627198576927185},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.45889827609062195},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.356781005859375},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22840014100074768},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.12892794609069824},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.11417779326438904},{"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/080742725","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080742725","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.372.5100","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.372.5100","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.archives-ouvertes.fr/docs/00/42/98/02/PDF/Pencils_Riccati_JUNGERS_09.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00429802v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00429802","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications, 2009, 31 (3), pp.1257-1278. ⟨10.1137/080742725⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00429802v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00429802","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications, 2009, 31 (3), pp.1257-1278. ⟨10.1137/080742725⟩","raw_type":"Journal articles"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.5}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W197984925","https://openalex.org/W1578630563","https://openalex.org/W1659904137","https://openalex.org/W1943587037","https://openalex.org/W1971495800","https://openalex.org/W1971499785","https://openalex.org/W1976384891","https://openalex.org/W1977386258","https://openalex.org/W1983184346","https://openalex.org/W1984452258","https://openalex.org/W1988849267","https://openalex.org/W2000661060","https://openalex.org/W2002357820","https://openalex.org/W2013348732","https://openalex.org/W2035094999","https://openalex.org/W2038370511","https://openalex.org/W2038585808","https://openalex.org/W2052323297","https://openalex.org/W2055300044","https://openalex.org/W2062697270","https://openalex.org/W2067050450","https://openalex.org/W2072792819","https://openalex.org/W2074675586","https://openalex.org/W2082559624","https://openalex.org/W2093090480","https://openalex.org/W2097327029","https://openalex.org/W2097509729","https://openalex.org/W2102352719","https://openalex.org/W2112878831","https://openalex.org/W2114047313","https://openalex.org/W2120459890","https://openalex.org/W2129288433","https://openalex.org/W2138688253","https://openalex.org/W2171413912","https://openalex.org/W3035578948","https://openalex.org/W4234761190"],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2105459831","https://openalex.org/W1546579375","https://openalex.org/W2127238600","https://openalex.org/W1563296412","https://openalex.org/W16457797","https://openalex.org/W2792258377","https://openalex.org/W2071397443","https://openalex.org/W2114047313","https://openalex.org/W4251980810"],"abstract_inverted_index":{"A":[0],"discrete-time":[1,13],"nonsymmetric":[2,14],"algebraic":[3,15],"Riccati":[4,16],"system":[5],"which":[6],"incorporates":[7],"as":[8],"special":[9],"cases":[10],"of":[11,47,51,63,82],"various":[12],"equations":[17],"is":[18,58],"introduced":[19],"and":[20,31],"studied":[21],"without":[22,75],"any":[23],"restrictive":[24],"assumptions":[25,78],"on":[26,79],"the":[27,40,61,76,80],"matrix":[28,54,84],"coefficients.":[29,85],"Necessary":[30],"sufficient":[32],"existence":[33],"conditions":[34],"together":[35],"with":[36,66],"computable":[37],"formulas":[38],"for":[39],"stabilizing":[41],"solution":[42],"are":[43],"given":[44],"in":[45,60],"terms":[46],"proper":[48],"deflating":[49],"subspaces":[50],"an":[52,67],"associated":[53],"pencil.":[55],"The":[56],"theory":[57,65],"applied":[59],"framework":[62],"game":[64],"open-loop":[68],"information":[69],"structure":[70],"to":[71],"design":[72],"Nash":[73],"strategy":[74],"classical":[77],"invertibility":[81],"some":[83]},"counts_by_year":[{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}