{"id":"https://openalex.org/W2946856397","doi":"https://doi.org/10.1177/0142331219836473","title":"From fractional-order to complex-order integrator loop gain: Robust control design and its stability analysis","display_name":"From fractional-order to complex-order integrator loop gain: Robust control design and its stability analysis","publication_year":2019,"publication_date":"2019-05-27","ids":{"openalex":"https://openalex.org/W2946856397","doi":"https://doi.org/10.1177/0142331219836473","mag":"2946856397"},"language":"en","primary_location":{"id":"doi:10.1177/0142331219836473","is_oa":false,"landing_page_url":"https://doi.org/10.1177/0142331219836473","pdf_url":null,"source":{"id":"https://openalex.org/S24148485","display_name":"Transactions of the Institute of Measurement and Control","issn_l":"0142-3312","issn":["0142-3312","1477-0369"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the Institute of Measurement and 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":null,"display_name":"Mohammad Reza Rahmani","orcid":"https://orcid.org/0000-0002-5430-5980"},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Mohammad Reza Rahmani","raw_affiliation_strings":["Electrical Engineering Department, Iran University of Science and Technology, Iran"],"raw_orcid":"https://orcid.org/0000-0002-5430-5980","affiliations":[{"raw_affiliation_string":"Electrical Engineering Department, Iran University of Science and Technology, Iran","institution_ids":["https://openalex.org/I67009956"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113789284","display_name":"Ali Jalali","orcid":null},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Ali Akbar Jalali","raw_affiliation_strings":["Electrical Engineering Department, Iran University of Science and Technology, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical Engineering Department, Iran University of Science and Technology, Iran","institution_ids":["https://openalex.org/I67009956"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I67009956"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.04835651,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"41","issue":"13","first_page":"3799","last_page":"3807"},"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/T14083","display_name":"Extremum Seeking Control Systems","score":0.9975000023841858,"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/T11749","display_name":"Iterative Learning Control Systems","score":0.9840999841690063,"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/control-theory","display_name":"Control theory (sociology)","score":0.7780323028564453},{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.6569860577583313},{"id":"https://openalex.org/keywords/fractional-order-system","display_name":"Fractional-order system","score":0.634933590888977},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6122258901596069},{"id":"https://openalex.org/keywords/nyquist-stability-criterion","display_name":"Nyquist stability criterion","score":0.5773906707763672},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.5590189695358276},{"id":"https://openalex.org/keywords/control-system","display_name":"Control system","score":0.5141375660896301},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4793054163455963},{"id":"https://openalex.org/keywords/bode-plot","display_name":"Bode plot","score":0.4641706943511963},{"id":"https://openalex.org/keywords/describing-function","display_name":"Describing function","score":0.45132532715797424},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4222496449947357},{"id":"https://openalex.org/keywords/frequency-response","display_name":"Frequency response","score":0.41679689288139343},{"id":"https://openalex.org/keywords/transfer-function","display_name":"Transfer function","score":0.4054257571697235},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30986008048057556},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2901414632797241},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.25947105884552},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.23262256383895874},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1940009891986847},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08114445209503174}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7780323028564453},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.6569860577583313},{"id":"https://openalex.org/C2779728712","wikidata":"https://www.wikidata.org/wiki/Q17014617","display_name":"Fractional-order system","level":3,"score":0.634933590888977},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6122258901596069},{"id":"https://openalex.org/C7630364","wikidata":"https://www.wikidata.org/wiki/Q1756793","display_name":"Nyquist stability criterion","level":3,"score":0.5773906707763672},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.5590189695358276},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.5141375660896301},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4793054163455963},{"id":"https://openalex.org/C92487091","wikidata":"https://www.wikidata.org/wiki/Q245627","display_name":"Bode plot","level":3,"score":0.4641706943511963},{"id":"https://openalex.org/C147317941","wikidata":"https://www.wikidata.org/wiki/Q1925419","display_name":"Describing function","level":3,"score":0.45132532715797424},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4222496449947357},{"id":"https://openalex.org/C8590192","wikidata":"https://www.wikidata.org/wiki/Q1054694","display_name":"Frequency response","level":2,"score":0.41679689288139343},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.4054257571697235},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30986008048057556},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2901414632797241},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.25947105884552},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.23262256383895874},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1940009891986847},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08114445209503174},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1177/0142331219836473","is_oa":false,"landing_page_url":"https://doi.org/10.1177/0142331219836473","pdf_url":null,"source":{"id":"https://openalex.org/S24148485","display_name":"Transactions of the Institute of Measurement and Control","issn_l":"0142-3312","issn":["0142-3312","1477-0369"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the Institute of Measurement and Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4399999976158142,"id":"https://metadata.un.org/sdg/14","display_name":"Life below water"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W89617744","https://openalex.org/W1850667745","https://openalex.org/W1992956754","https://openalex.org/W2003092572","https://openalex.org/W2006193826","https://openalex.org/W2012140399","https://openalex.org/W2012417193","https://openalex.org/W2029678503","https://openalex.org/W2033177809","https://openalex.org/W2076903979","https://openalex.org/W2081399981","https://openalex.org/W2084119616","https://openalex.org/W2084209819","https://openalex.org/W2084511080","https://openalex.org/W2103917488","https://openalex.org/W2109607362","https://openalex.org/W2110643194","https://openalex.org/W2110646088","https://openalex.org/W2111349079","https://openalex.org/W2112389638","https://openalex.org/W2114388612","https://openalex.org/W2119251202","https://openalex.org/W2126535736","https://openalex.org/W2129397322","https://openalex.org/W2138958178","https://openalex.org/W2140214426","https://openalex.org/W2148453544","https://openalex.org/W2154709196","https://openalex.org/W2161411167","https://openalex.org/W2257204441","https://openalex.org/W2259227674","https://openalex.org/W2313124004","https://openalex.org/W2593904818","https://openalex.org/W2741253835","https://openalex.org/W2765641107","https://openalex.org/W2770906696","https://openalex.org/W2788707115","https://openalex.org/W2793273438","https://openalex.org/W2809473270","https://openalex.org/W2809484026","https://openalex.org/W2954916131","https://openalex.org/W3105084698","https://openalex.org/W4232986545","https://openalex.org/W4250288205","https://openalex.org/W4283658368"],"related_works":["https://openalex.org/W2000331798","https://openalex.org/W2903303226","https://openalex.org/W18072180","https://openalex.org/W3135784819","https://openalex.org/W2974315285","https://openalex.org/W4311925403","https://openalex.org/W4285137703","https://openalex.org/W3117847546","https://openalex.org/W2130342816","https://openalex.org/W656464541"],"abstract_inverted_index":{"Complex-order":[0],"differintegral":[1,13,29],"(COD)":[2],"is":[3,37,46,75,99,112,118,129,142],"the":[4,12,31,35,39,53,57,63,69,81,84,93,108,122,125,132,145,148,160,165],"extended":[5],"version":[6],"of":[7,34,42,49,52,56,65,68,83,95,103,107,124,147,164],"fractional-order":[8,28],"one":[9],"in":[10,136],"which":[11],"order":[14,55],"can":[15],"be":[16,134],"a":[17,22,47,71,100,114,137],"complex":[18,54],"number":[19],"rather":[20],"than":[21],"real":[23],"number.":[24],"In":[25,59],"comparison":[26],"with":[27],"(FOD),":[30],"distinguishing":[32],"feature":[33],"COD":[36,133],"that":[38,120,131,141],"phase":[40,94],"slope":[41],"its":[43],"Bode":[44],"diagram":[45],"function":[48,102],"imaginary":[50],"part":[51],"COD.":[58],"this":[60,66],"paper,":[61],"by":[62,144],"use":[64,146],"property":[67],"COD,":[70],"robust":[72],"control":[73,88,110,126,168],"system":[74,89,111],"proposed.":[76],"The":[77],"design":[78],"procedure":[79],"and":[80,162],"realization":[82],"proposed":[85,109,166],"COD-based":[86],"closed-loop":[87],"are":[90,156],"discussed.":[91],"Since":[92],"COD\u2019s":[96],"frequency":[97,139],"response":[98],"nonsymmetric":[101],"frequency,":[104],"stability":[105,123,150],"analysis":[106],"considered":[113],"problematic":[115],"task.":[116],"It":[117],"proven":[119],"for":[121],"system,":[127],"it":[128],"essential":[130],"applied":[135],"limited":[138],"band":[140],"derived":[143],"Nyquist":[149],"criterion.":[151],"Finally,":[152],"some":[153],"numerical":[154],"examples":[155],"given":[157],"to":[158],"demonstrate":[159],"validity":[161],"superiority":[163],"complex-order":[167],"system.":[169]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}