{"id":"https://openalex.org/W1979605014","doi":"https://doi.org/10.1016/0005-1098(91)90136-p","title":"Study of the discrete singularly perturbed linear-quadratic control problem by a bilinear transformation","display_name":"Study of the discrete singularly perturbed linear-quadratic control problem by a bilinear transformation","publication_year":1991,"publication_date":"1991-11-01","ids":{"openalex":"https://openalex.org/W1979605014","doi":"https://doi.org/10.1016/0005-1098(91)90136-p","mag":"1979605014"},"language":"en","primary_location":{"id":"doi:10.1016/0005-1098(91)90136-p","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0005-1098(91)90136-p","pdf_url":null,"source":{"id":"https://openalex.org/S51360982","display_name":"Automatica","issn_l":"0005-1098","issn":["0005-1098","1873-2836"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automatica","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/A5031375377","display_name":"Zoran Gaji\u0107","orcid":"https://orcid.org/0000-0002-0187-6181"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]},{"id":"https://openalex.org/I4210109165","display_name":"Environmental and Occupational Health Sciences Institute","ror":"https://ror.org/01vta4r13","country_code":"US","type":"education","lineage":["https://openalex.org/I4210109165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zoran Gajic","raw_affiliation_strings":["Rutgers University, Department of Electrical and Computer Engineering, Piscataway, NJ 08855-0909, U.S.A","Rutgers University, Department of electrical and Computer Engineering, Piscataway, NJ 08855-0909, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rutgers University, Department of Electrical and Computer Engineering, Piscataway, NJ 08855-0909, U.S.A","institution_ids":["https://openalex.org/I102322142","https://openalex.org/I4210109165"]},{"raw_affiliation_string":"Rutgers University, Department of electrical and Computer Engineering, Piscataway, NJ 08855-0909, U.S.A","institution_ids":["https://openalex.org/I102322142","https://openalex.org/I4210109165"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100773343","display_name":"Xuemin Shen","orcid":"https://orcid.org/0000-0002-4140-287X"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]},{"id":"https://openalex.org/I4210109165","display_name":"Environmental and Occupational Health Sciences Institute","ror":"https://ror.org/01vta4r13","country_code":"US","type":"education","lineage":["https://openalex.org/I4210109165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xue-Min Shen","raw_affiliation_strings":["Rutgers University, Department of Electrical and Computer Engineering, Piscataway, NJ 08855-0909, U.S.A","Rutgers University, Department of electrical and Computer Engineering, Piscataway, NJ 08855-0909, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rutgers University, Department of Electrical and Computer Engineering, Piscataway, NJ 08855-0909, U.S.A","institution_ids":["https://openalex.org/I102322142","https://openalex.org/I4210109165"]},{"raw_affiliation_string":"Rutgers University, Department of electrical and Computer Engineering, Piscataway, NJ 08855-0909, U.S.A","institution_ids":["https://openalex.org/I102322142","https://openalex.org/I4210109165"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3500,"currency":"USD","value_usd":3500},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.11780973,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"6","first_page":"1025","last_page":"1028"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9959999918937683,"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"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9959999918937683,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9452999830245972,"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/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.6855143308639526},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6773064136505127},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.6572284698486328},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.6451419591903687},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5764376521110535},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5434014201164246},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.5388280153274536},{"id":"https://openalex.org/keywords/bilinear-transform","display_name":"Bilinear transform","score":0.5336212515830994},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5332496166229248},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5267177224159241},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4835807681083679},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4659968614578247},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.44794559478759766},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.44274380803108215},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.37486958503723145},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36290284991264343},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3203921318054199},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.237726092338562},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20903164148330688},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1610700786113739},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14190781116485596},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.07521480321884155}],"concepts":[{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.6855143308639526},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6773064136505127},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.6572284698486328},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.6451419591903687},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5764376521110535},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5434014201164246},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.5388280153274536},{"id":"https://openalex.org/C109786386","wikidata":"https://www.wikidata.org/wiki/Q861804","display_name":"Bilinear transform","level":4,"score":0.5336212515830994},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5332496166229248},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5267177224159241},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4835807681083679},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4659968614578247},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.44794559478759766},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.44274380803108215},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.37486958503723145},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36290284991264343},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3203921318054199},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.237726092338562},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20903164148330688},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1610700786113739},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14190781116485596},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.07521480321884155},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"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/C36390408","wikidata":"https://www.wikidata.org/wiki/Q1163067","display_name":"Digital filter","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0005-1098(91)90136-p","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0005-1098(91)90136-p","pdf_url":null,"source":{"id":"https://openalex.org/S51360982","display_name":"Automatica","issn_l":"0005-1098","issn":["0005-1098","1873-2836"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automatica","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W632941928","https://openalex.org/W2001105076","https://openalex.org/W2011489460","https://openalex.org/W2024446871","https://openalex.org/W2036321067","https://openalex.org/W2041947785","https://openalex.org/W2044837789","https://openalex.org/W2045876621","https://openalex.org/W2058045317","https://openalex.org/W2071484676","https://openalex.org/W2125963130","https://openalex.org/W2129551182","https://openalex.org/W2130545484","https://openalex.org/W2156768156","https://openalex.org/W2170938079","https://openalex.org/W2531590621","https://openalex.org/W6620271486","https://openalex.org/W6679325236","https://openalex.org/W6926355872"],"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":null,"counts_by_year":[],"updated_date":"2026-06-20T20:08:15.867695","created_date":"2025-10-10T00:00:00"}