{"id":"https://openalex.org/W1977355413","doi":"https://doi.org/10.1080/00207720410001734237","title":"Model reduction of bilinear systems described by input\u2013output difference equation","display_name":"Model reduction of bilinear systems described by input\u2013output difference equation","publication_year":2004,"publication_date":"2004-07-20","ids":{"openalex":"https://openalex.org/W1977355413","doi":"https://doi.org/10.1080/00207720410001734237","mag":"1977355413"},"language":"en","primary_location":{"id":"doi:10.1080/00207720410001734237","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207720410001734237","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","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/A5032596551","display_name":"S.A. Al-Baiyat","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"S. A. Al-Baiyat","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5032596551"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.07480352,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"35","issue":"9","first_page":"503","last_page":"510"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9998999834060669,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9990000128746033,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9922999739646912,"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/mathematics","display_name":"Mathematics","score":0.7715620994567871},{"id":"https://openalex.org/keywords/hankel-matrix","display_name":"Hankel matrix","score":0.7079710960388184},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.7060186862945557},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.6708801984786987},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.6543638706207275},{"id":"https://openalex.org/keywords/matrix-difference-equation","display_name":"Matrix difference equation","score":0.6192214488983154},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.5351513028144836},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5246608257293701},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4922608435153961},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.4842800498008728},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4688578248023987},{"id":"https://openalex.org/keywords/state-space-representation","display_name":"State-space representation","score":0.4598991870880127},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.43312638998031616},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.42290446162223816},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.38757604360580444},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30470579862594604},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28418922424316406},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.2810021638870239},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.24554938077926636},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14230391383171082},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.11687034368515015}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7715620994567871},{"id":"https://openalex.org/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"score":0.7079710960388184},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.7060186862945557},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.6708801984786987},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6543638706207275},{"id":"https://openalex.org/C47285271","wikidata":"https://www.wikidata.org/wiki/Q6787869","display_name":"Matrix difference equation","level":4,"score":0.6192214488983154},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.5351513028144836},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5246608257293701},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4922608435153961},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.4842800498008728},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4688578248023987},{"id":"https://openalex.org/C52918065","wikidata":"https://www.wikidata.org/wiki/Q230945","display_name":"State-space representation","level":2,"score":0.4598991870880127},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.43312638998031616},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.42290446162223816},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.38757604360580444},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30470579862594604},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28418922424316406},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2810021638870239},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.24554938077926636},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14230391383171082},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.11687034368515015},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207720410001734237","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207720410001734237","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","raw_type":"journal-article"},{"id":"pmh:oai::450","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400553","display_name":"Munich Personal RePEc Archive (Ludwig Maximilian University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I8204097","host_organization_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","host_organization_lineage":["https://openalex.org/I8204097"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1568991775","https://openalex.org/W1964815380","https://openalex.org/W1993300095","https://openalex.org/W2009180289","https://openalex.org/W2027110594","https://openalex.org/W2053124524","https://openalex.org/W2053904120","https://openalex.org/W2064733273","https://openalex.org/W2065902930","https://openalex.org/W2066913503","https://openalex.org/W2069049088","https://openalex.org/W2079665343","https://openalex.org/W2085724310","https://openalex.org/W2090361488","https://openalex.org/W2104371559","https://openalex.org/W2107886288","https://openalex.org/W2117861373","https://openalex.org/W2128247688","https://openalex.org/W2143588377","https://openalex.org/W2151186717","https://openalex.org/W2166689793","https://openalex.org/W2172066780","https://openalex.org/W2562166486","https://openalex.org/W2563054324"],"related_works":["https://openalex.org/W4319586039","https://openalex.org/W3195533526","https://openalex.org/W4382583540","https://openalex.org/W2147072251","https://openalex.org/W2148568324","https://openalex.org/W4387899112","https://openalex.org/W2150699280","https://openalex.org/W4285156762","https://openalex.org/W3200162719","https://openalex.org/W4241783538"],"abstract_inverted_index":{"A":[0,17,84],"class":[1],"of":[2,24,31,34,45,80,93],"single":[3,5],"input":[4],"output":[6],"bilinear":[7,62],"systems":[8],"described":[9],"by":[10],"their":[11],"input-output":[12],"difference":[13,35],"equation":[14],"is":[15,27,50,55,87],"considered.":[16],"simple":[18],"expression":[19],"for":[20],"the":[21,25,32,41,81,91,94],"Volterra":[22],"kernels":[23],"system":[26],"derived":[28],"in":[29],"terms":[30],"coefficients":[33],"equation.":[36],"An":[37],"algorithm,":[38],"based":[39],"on":[40],"singular":[42],"value":[43],"decomposition":[44],"a":[46,60],"generalized":[47],"Hankel":[48,66],"matrix,":[49],"also":[51],"developed.":[52],"The":[53,65],"algorithm":[54],"then":[56],"used":[57],"to":[58,89],"find":[59],"reduced-order":[61],"state-space":[63,82],"model.":[64],"approach":[67],"will":[68],"be":[69],"extensively":[70],"studied":[71],"under":[72],"different":[73,78],"data":[74],"length":[75],"cases":[76],"and":[77],"orders":[79],"models.":[83],"numerical":[85],"example":[86],"presented":[88],"illustrate":[90],"effectiveness":[92],"proposed":[95],"algorithm.":[96]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
