{"id":"https://openalex.org/W2117364303","doi":"https://doi.org/10.1109/mmar.2011.6031331","title":"On the rational approximation of fractional order systems","display_name":"On the rational approximation of fractional order systems","publication_year":2011,"publication_date":"2011-08-01","ids":{"openalex":"https://openalex.org/W2117364303","doi":"https://doi.org/10.1109/mmar.2011.6031331","mag":"2117364303"},"language":"en","primary_location":{"id":"doi:10.1109/mmar.2011.6031331","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mmar.2011.6031331","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 16th International Conference on Methods &amp; Models in Automation &amp; Robotics","raw_type":"proceedings-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/A5111770942","display_name":"Wies\u0142aw Krajewski","orcid":null},"institutions":[{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"funder","lineage":["https://openalex.org/I99542240"]},{"id":"https://openalex.org/I66083562","display_name":"Systems Research Institute","ror":"https://ror.org/0111cp837","country_code":"PL","type":"facility","lineage":["https://openalex.org/I66083562","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Wieslaw Krajewski","raw_affiliation_strings":["Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland","Systems Research Institute, Polish Academy of Sciences, Ul. Newelska 6, 01-447 Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland","institution_ids":["https://openalex.org/I66083562","https://openalex.org/I99542240"]},{"raw_affiliation_string":"Systems Research Institute, Polish Academy of Sciences, Ul. Newelska 6, 01-447 Warsaw, Poland","institution_ids":["https://openalex.org/I66083562","https://openalex.org/I99542240"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067116263","display_name":"Umberto Viaro","orcid":"https://orcid.org/0000-0001-8400-7397"},"institutions":[{"id":"https://openalex.org/I129043915","display_name":"University of Udine","ror":"https://ror.org/05ht0mh31","country_code":"IT","type":"education","lineage":["https://openalex.org/I129043915"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Umberto Viaro","raw_affiliation_strings":["Dipartimento di Ingegneria Elettrica, Universit\u00e0 degli Studi di Udine, Udine, Italy","Dipartimento di Ingegneria Elettrica, Gestionale e Meccanica, Universit\u00e0 degli Studi di Udine, Via delle Scienze 208, 33100 Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria Elettrica, Universit\u00e0 degli Studi di Udine, Udine, Italy","institution_ids":["https://openalex.org/I129043915"]},{"raw_affiliation_string":"Dipartimento di Ingegneria Elettrica, Gestionale e Meccanica, Universit\u00e0 degli Studi di Udine, Via delle Scienze 208, 33100 Italy","institution_ids":["https://openalex.org/I129043915"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111770942"],"corresponding_institution_ids":["https://openalex.org/I66083562","https://openalex.org/I99542240"],"apc_list":null,"apc_paid":null,"fwci":0.6525,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.77721681,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"132","last_page":"136"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","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/T11081","display_name":"Advanced Control Systems Design","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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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":0.9959999918937683,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5888685584068298},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.5803471803665161},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5726009607315063},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5457378029823303},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5356319546699524},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5288715958595276},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4788051247596741},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44918546080589294},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4459807276725769},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.4329175353050232},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4305087924003601},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3229520916938782},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28490307927131653},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.26587972044944763},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.26398926973342896}],"concepts":[{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5888685584068298},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.5803471803665161},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5726009607315063},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5457378029823303},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5356319546699524},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5288715958595276},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4788051247596741},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44918546080589294},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4459807276725769},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.4329175353050232},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4305087924003601},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3229520916938782},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28490307927131653},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26587972044944763},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26398926973342896},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/mmar.2011.6031331","is_oa":false,"landing_page_url":"https://doi.org/10.1109/mmar.2011.6031331","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 16th International Conference on Methods &amp; Models in Automation &amp; Robotics","raw_type":"proceedings-article"},{"id":"pmh:oai:air.uniud.it:11390/883092","is_oa":false,"landing_page_url":"http://hdl.handle.net/11390/883092","pdf_url":null,"source":{"id":"https://openalex.org/S4306401163","display_name":"Institutional Research Information System (University of Udine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I129043915","host_organization_name":"University of Udine","host_organization_lineage":["https://openalex.org/I129043915"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"4.1 Contributo in Atti di convegno"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W204072296","https://openalex.org/W207094665","https://openalex.org/W837933214","https://openalex.org/W1578028990","https://openalex.org/W1651861097","https://openalex.org/W1968270757","https://openalex.org/W1969260675","https://openalex.org/W1969313263","https://openalex.org/W2007422900","https://openalex.org/W2008761299","https://openalex.org/W2009109764","https://openalex.org/W2066723487","https://openalex.org/W2068721678","https://openalex.org/W2120090534","https://openalex.org/W2122289962","https://openalex.org/W2140748343","https://openalex.org/W2151622640","https://openalex.org/W2157337908","https://openalex.org/W2157347895","https://openalex.org/W2161411167","https://openalex.org/W2787959293","https://openalex.org/W3041627693","https://openalex.org/W4285719527","https://openalex.org/W6634629539","https://openalex.org/W6678328328"],"related_works":["https://openalex.org/W2056609367","https://openalex.org/W2123804044","https://openalex.org/W189372398","https://openalex.org/W2370664448","https://openalex.org/W2061149031","https://openalex.org/W2094002148","https://openalex.org/W2076338521","https://openalex.org/W4318473088","https://openalex.org/W2883183014","https://openalex.org/W2068392195"],"abstract_inverted_index":{"This":[0,56],"paper":[1],"is":[2,20,54,58],"concerned":[3],"with":[4,103],"the":[5,23,40,43,47,75,98,109,112],"finite-dimensional":[6],"approximation":[7,89],"of":[8,42,46,77],"a":[9,28,32,50,62,69],"fractional-order":[10,29,48],"system":[11],"represented":[12],"in":[13,61,108],"state-space":[14,63],"form.":[15],"To":[16,73],"this":[17,37,78],"purpose,":[18],"resort":[19],"made":[21],"to":[22,39,111],"Oustaloup":[24],"method":[25,38,83],"for":[26,84],"approximating":[27],"integrator":[30],"by":[31],"rational":[33],"filter.":[34],"By":[35],"applying":[36],"RHS":[41],"state":[44,66],"equation":[45,53,57],"system,":[49],"matrix":[51,67],"differential":[52],"obtained.":[55],"then":[59],"realized":[60],"form":[64],"whose":[65],"exhibits":[68],"(sparse)":[70],"block-companion":[71],"structure.":[72],"reduce":[74],"dimension":[76],"integer-order":[79],"model,":[80],"an":[81],"efficient":[82],"L":[85],"<inf":[86],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[87],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</inf>":[88],"can":[90],"profitably":[91],"be":[92],"applied.":[93],"Numerical":[94],"simulations":[95],"show":[96],"that":[97],"suggested":[99],"approach":[100],"compares":[101],"favourably":[102],"alternative":[104],"techniques":[105],"recently":[106],"presented":[107],"literature":[110],"same":[113],"purpose.":[114]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}