{"id":"https://openalex.org/W1979273932","doi":"https://doi.org/10.1137/090753048","title":"The Minimal State Space Realization for a Class of Fractional Order Transfer Functions","display_name":"The Minimal State Space Realization for a Class of Fractional Order Transfer Functions","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1979273932","doi":"https://doi.org/10.1137/090753048","mag":"1979273932"},"language":"en","primary_location":{"id":"doi:10.1137/090753048","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090753048","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","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/A5083512761","display_name":"Mahsan Tavakoli\u2010Kakhki","orcid":"https://orcid.org/0000-0001-6851-1614"},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mahsan Tavakoli-Kakhki","raw_affiliation_strings":["mah_tavakoli@ee.sharif.edu and haeri@sina.sharif.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"mah_tavakoli@ee.sharif.edu and haeri@sina.sharif.edu#TAB#","institution_ids":["https://openalex.org/I133529467"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071064795","display_name":"\u0621Mohammad Haeri","orcid":"https://orcid.org/0000-0001-8509-4525"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mohammad Haeri","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.7502,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.97292563,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"48","issue":"7","first_page":"4317","last_page":"4326"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9865000247955322,"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/T14083","display_name":"Extremum Seeking Control Systems","score":0.986299991607666,"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":0.8702641725540161},{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.8569594621658325},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.7165110111236572},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6864117383956909},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6407855749130249},{"id":"https://openalex.org/keywords/minimal-realization","display_name":"Minimal realization","score":0.6044016480445862},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.5987212657928467},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5828019976615906},{"id":"https://openalex.org/keywords/transfer-function","display_name":"Transfer function","score":0.5747010707855225},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5720150470733643},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5323118567466736},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.522110104560852},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.521943986415863},{"id":"https://openalex.org/keywords/transfer","display_name":"Transfer (computing)","score":0.4589053988456726},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3467981219291687},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32381725311279297},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.104164719581604},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.09377801418304443},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07503974437713623}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8702641725540161},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.8569594621658325},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7165110111236572},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6864117383956909},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6407855749130249},{"id":"https://openalex.org/C205609532","wikidata":"https://www.wikidata.org/wiki/Q770324","display_name":"Minimal realization","level":3,"score":0.6044016480445862},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.5987212657928467},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5828019976615906},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.5747010707855225},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5720150470733643},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5323118567466736},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.522110104560852},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.521943986415863},{"id":"https://openalex.org/C2776175482","wikidata":"https://www.wikidata.org/wiki/Q1195816","display_name":"Transfer (computing)","level":2,"score":0.4589053988456726},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3467981219291687},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32381725311279297},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.104164719581604},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.09377801418304443},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07503974437713623},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/090753048","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090753048","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.5199999809265137,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W806633968","https://openalex.org/W1991538949","https://openalex.org/W2009109764","https://openalex.org/W2041916474","https://openalex.org/W2068812300","https://openalex.org/W2087975056","https://openalex.org/W2117220239","https://openalex.org/W2126535736","https://openalex.org/W2143270297","https://openalex.org/W2149754660","https://openalex.org/W2163511830"],"related_works":["https://openalex.org/W2621018750","https://openalex.org/W1964957286","https://openalex.org/W2075723707","https://openalex.org/W1559020141","https://openalex.org/W2007960014","https://openalex.org/W2142399832","https://openalex.org/W1978743646","https://openalex.org/W2041504474","https://openalex.org/W2128933497","https://openalex.org/W2157374935"],"abstract_inverted_index":{"In":[0,60],"this":[1,61],"paper,":[2],"the":[3,17,33,40,55,63,84],"minimal":[4,87],"state":[5],"space":[6],"realization":[7],"of":[8,19,42,57,74,86],"a":[9,43,71,94],"fractional":[10,75],"order":[11,76],"transfer":[12,77],"function":[13],"is":[14,29,47,96],"investigated":[15],"in":[16],"sense":[18],"inner":[20,90],"dimension":[21,91],"both":[22],"for":[23,70],"commensurate":[24,44],"and":[25,65],"incommensurate":[26,58],"cases.":[27],"It":[28],"shown":[30],"that":[31],"while":[32],"traditional":[34],"tools":[35],"are":[36,68],"applicable":[37],"to":[38,51,106],"check":[39],"minimality":[41,56],"realization,":[45],"there":[46],"no":[48],"specific":[49,72],"procedure":[50],"be":[52,104],"certain":[53],"about":[54],"realizations.":[59],"regard,":[62],"necessary":[64],"sufficient":[66],"conditions":[67],"obtained":[69],"class":[73],"functions":[78],"by":[79],"which":[80,99],"one":[81],"can":[82,103],"verify":[83],"existence":[85],"realizations":[88,102],"with":[89],"2.":[92],"Furthermore,":[93],"transformation":[95],"introduced":[97],"through":[98],"all":[100],"these":[101],"transformed":[105],"each":[107],"other.":[108]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
