{"id":"https://openalex.org/W1990059832","doi":"https://doi.org/10.1109/tac.2013.2295661","title":"Frequency-Interval Model Reduction of Bilinear Systems","display_name":"Frequency-Interval Model Reduction of Bilinear Systems","publication_year":2014,"publication_date":"2014-01-31","ids":{"openalex":"https://openalex.org/W1990059832","doi":"https://doi.org/10.1109/tac.2013.2295661","mag":"1990059832"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2013.2295661","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2013.2295661","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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/A5089265820","display_name":"Hamid Reza Shaker","orcid":"https://orcid.org/0000-0003-2858-8400"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hamid Reza Shaker","raw_affiliation_strings":["Faculty of Engineering and Natural Sciences, Aalesund University College, \u00c5lesund, Norway"],"affiliations":[{"raw_affiliation_string":"Faculty of Engineering and Natural Sciences, Aalesund University College, \u00c5lesund, Norway","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018712800","display_name":"Maryamsadat Tahavori","orcid":"https://orcid.org/0000-0002-2407-6101"},"institutions":[{"id":"https://openalex.org/I891191580","display_name":"Aalborg University","ror":"https://ror.org/04m5j1k67","country_code":"DK","type":"education","lineage":["https://openalex.org/I891191580"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Maryamsadat Tahavori","raw_affiliation_strings":["Department of Electronic Systems, Aalborg University, Aalborg, Denmark","Dept. of Electronic Systems, Aalborg University, Aalborg, Denmark#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Systems, Aalborg University, Aalborg, Denmark","institution_ids":["https://openalex.org/I891191580"]},{"raw_affiliation_string":"Dept. of Electronic Systems, Aalborg University, Aalborg, Denmark#TAB#","institution_ids":["https://openalex.org/I891191580"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089265820"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.0922,"has_fulltext":false,"cited_by_count":47,"citation_normalized_percentile":{"value":0.9676335,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"59","issue":"7","first_page":"1948","last_page":"1953"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998000264167786,"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":0.9998000264167786,"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/T11372","display_name":"Hydraulic and Pneumatic Systems","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T11236","display_name":"Control Systems and Identification","score":0.9639999866485596,"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/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.726214587688446},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7141431570053101},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6417302489280701},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.6157058477401733},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5382620096206665},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.46925613284111023},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.430032342672348},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.42364197969436646},{"id":"https://openalex.org/keywords/observability","display_name":"Observability","score":0.412864625453949},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.20025524497032166},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19120848178863525}],"concepts":[{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.726214587688446},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7141431570053101},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6417302489280701},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6157058477401733},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5382620096206665},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.46925613284111023},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.430032342672348},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.42364197969436646},{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.412864625453949},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.20025524497032166},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19120848178863525},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2013.2295661","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2013.2295661","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/cf774780-5812-48e4-a13a-4a26b22d98fa","is_oa":false,"landing_page_url":"https://vbn.aau.dk/da/publications/cf774780-5812-48e4-a13a-4a26b22d98fa","pdf_url":null,"source":{"id":"https://openalex.org/S4306401731","display_name":"VBN Forskningsportal (Aalborg Universitet)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I891191580","host_organization_name":"Aalborg University","host_organization_lineage":["https://openalex.org/I891191580"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Shaker , H R & Tahavori , M 2014 , ' Frequency-interval model reduction of bilinear systems ' , IEEE Transactions on Automatic Control , vol. 59 , no. 7 , 6690103 , pp. 1948-1953 . https://doi.org/10.1109/TAC.2013.2295661","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1530239534","https://openalex.org/W1551480811","https://openalex.org/W1969325212","https://openalex.org/W1973799947","https://openalex.org/W1985927505","https://openalex.org/W1988376519","https://openalex.org/W2002858896","https://openalex.org/W2009180289","https://openalex.org/W2027110594","https://openalex.org/W2050759541","https://openalex.org/W2064733273","https://openalex.org/W2069049088","https://openalex.org/W2081604815","https://openalex.org/W2088872157","https://openalex.org/W2101610188","https://openalex.org/W2103960654","https://openalex.org/W2128247688","https://openalex.org/W2133642820","https://openalex.org/W2138190945","https://openalex.org/W2155982947","https://openalex.org/W2166365900","https://openalex.org/W2172066780","https://openalex.org/W2318945581","https://openalex.org/W2492791808","https://openalex.org/W2563054324","https://openalex.org/W6699364840"],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W2383986032","https://openalex.org/W2030955003","https://openalex.org/W2374426356","https://openalex.org/W2059628530","https://openalex.org/W2164487476","https://openalex.org/W3194517843","https://openalex.org/W1977987201","https://openalex.org/W2106169668","https://openalex.org/W2534107666"],"abstract_inverted_index":{"In":[0],"this":[1,38],"technical":[2],"note,":[3],"a":[4,31,34],"new":[5,40],"method":[6,16,86,103],"for":[7,21,46,67],"model":[8],"reduction":[9],"of":[10,93],"bilinear":[11,47],"systems":[12],"is":[13,17,27,50,78,87,104,112],"presented.":[14],"The":[15,65,85,97],"developed":[18],"in":[19,24,33],"particular":[20],"many":[22],"applications":[23],"which":[25,111],"one":[26],"interested":[28],"to":[29,58,70,80],"approximate":[30],"system":[32],"given":[35],"frequency-interval.":[36],"To":[37],"end,":[39],"generalized":[41,62],"frequency-interval":[42,61],"gramians":[43,54],"are":[44,55,73],"introduced":[45],"systems.":[48],"It":[49],"shown":[51],"that":[52,101],"these":[53,68],"the":[56,59,91,102,115],"solutions":[57],"so-called":[60],"Lyapunov":[63],"equations.":[64],"conditions":[66],"equations":[69,83],"be":[71],"solvable":[72],"derived":[74],"and":[75],"an":[76,94],"algorithm":[77],"proposed":[79],"solve":[81],"such":[82],"iteratively.":[84],"further":[88],"illustrated":[89],"with":[90],"help":[92],"illustrative":[95],"example.":[96],"numerical":[98],"results":[99],"show":[100],"more":[105],"accurate":[106],"than":[107],"its":[108],"previous":[109],"counterpart":[110],"based":[113],"on":[114],"ordinary":[116],"gramians.":[117]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}