{"id":"https://openalex.org/W1547460053","doi":"https://doi.org/10.23919/ecc.2001.7076129","title":"Application of diffusive representations to discretized fractional systems: Stability, positivity and simulations issues","display_name":"Application of diffusive representations to discretized fractional systems: Stability, positivity and simulations issues","publication_year":2001,"publication_date":"2001-09-01","ids":{"openalex":"https://openalex.org/W1547460053","doi":"https://doi.org/10.23919/ecc.2001.7076129","mag":"1547460053"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.2001.7076129","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2001.7076129","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2001 European Control Conference (ECC)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5044570096","display_name":"Gabriel Dauphin","orcid":"https://orcid.org/0000-0002-0677-6702"},"institutions":[{"id":"https://openalex.org/I12356871","display_name":"T\u00e9l\u00e9com Paris","ror":"https://ror.org/01naq7912","country_code":"FR","type":"education","lineage":["https://openalex.org/I12356871","https://openalex.org/I205703379","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"G. Dauphin","raw_affiliation_strings":["ENST, TSI dept. &amp; CNRS, URA 820 46, rue Barrault F-75634 Paris Cedex 13, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ENST, TSI dept. &amp; CNRS, URA 820 46, rue Barrault F-75634 Paris Cedex 13, France","institution_ids":["https://openalex.org/I12356871","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023725587","display_name":"Denis Matignon","orcid":"https://orcid.org/0000-0002-0729-4609"},"institutions":[{"id":"https://openalex.org/I12356871","display_name":"T\u00e9l\u00e9com Paris","ror":"https://ror.org/01naq7912","country_code":"FR","type":"education","lineage":["https://openalex.org/I12356871","https://openalex.org/I205703379","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"D. Matignon","raw_affiliation_strings":["ENST, TSI dept. &amp; CNRS, URA 820 46, rue Barrault F-75634 Paris Cedex 13, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ENST, TSI dept. &amp; CNRS, URA 820 46, rue Barrault F-75634 Paris Cedex 13, France","institution_ids":["https://openalex.org/I12356871","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1147541,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1490","last_page":"1495"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9994999766349792,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9933000206947327,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7141185998916626},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6809254884719849},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6721969842910767},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5091280341148376},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.4726794362068176},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.45964479446411133},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41208139061927795},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35222116112709045},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3469299376010895},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13710835576057434},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10271954536437988},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08524370193481445}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7141185998916626},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6809254884719849},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6721969842910767},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5091280341148376},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4726794362068176},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.45964479446411133},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41208139061927795},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35222116112709045},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3469299376010895},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13710835576057434},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10271954536437988},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08524370193481445},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/ecc.2001.7076129","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2001.7076129","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2001 European Control Conference (ECC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8600000143051147,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W99253999","https://openalex.org/W585909976","https://openalex.org/W1530054495","https://openalex.org/W1545269727","https://openalex.org/W2019424969","https://openalex.org/W2063493327","https://openalex.org/W2095477585","https://openalex.org/W2121768877","https://openalex.org/W2124357853","https://openalex.org/W2125793838","https://openalex.org/W3042995841"],"related_works":["https://openalex.org/W2150830839","https://openalex.org/W2123102751","https://openalex.org/W2376419853","https://openalex.org/W2946566599","https://openalex.org/W2100428849","https://openalex.org/W2579663521","https://openalex.org/W2012038446","https://openalex.org/W2973336026","https://openalex.org/W2037063555","https://openalex.org/W3042639525"],"abstract_inverted_index":{"Continuous-time":[0],"fractional":[1,38,93,130,149],"transfer":[2],"functions":[3],"such":[4,65],"as":[5,109],"s-\u03b1have":[6],"been":[7,42],"studied":[8],"from":[9,99,124],"many":[10],"viewpoints.":[11],"Diffusive":[12],"representations":[13,67],"have":[14,40],"given":[15],"an":[16,174],"infinite-dimensional":[17],"realization":[18],"for":[19,33,182],"these":[20],"operators;":[21],"this":[22,59],"is":[23,61,159],"a":[24,87,92,104,120,152,162],"new":[25,50],"framework":[26,51],"that":[27,178],"reveals":[28],"dissipativity":[29],"and":[30,44,78,119,151,169],"proves":[31],"useful":[32],"numerical":[34],"approximations.":[35],"Similarly,":[36],"discrete-time":[37,53],"filters":[39],"already":[41],"studied,":[43],"can":[45,68,139],"be":[46,69,140],"recast":[47],"in":[48],"the":[49,82,110,113,117,125,129,136,148,156,165,170,183],"of":[52,58,81,112,116,128,147,173],"diffusive":[54,66,126],"representations.":[55],"The":[56],"aim":[57],"paper":[60],"to":[62,71],"show":[63],"how":[64],"used":[70],"analyse":[72],"two":[73],"different":[74],"discretizations":[75],"(backward":[76],"difference":[77],"impulse":[79],"invariance)":[80],"same":[83],"continuous-time":[84],"system,":[85],"namely":[86],"standard":[88],"oscillator":[89,118],"damped":[90],"by":[91,161],"operator.":[94],"-":[95,132],"Internal":[96],"stability":[97,134],"stems":[98],"LaSalle":[100],"invariance":[101],"principle":[102],"with":[103],"global":[105,184],"Lyapunov":[106],"functional":[107],"defined":[108],"sum":[111],"mechanical":[114],"energy":[115,137],"storage":[121],"function":[122],"built":[123],"representation":[127],"damping.":[131],"External":[133],"(in":[135],"sense)":[138],"proved":[141],"using":[142],"strong":[143,171],"positivity":[144,172],"(i.e.":[145],"coercivity)":[146],"damping":[150],"passivity":[153],"theorem.":[154],"When":[155],"coupling":[157],"parameter":[158],"replaced":[160],"memoryless":[163],"nonlinearity,":[164],"small":[166],"gain":[167],"theorem":[168],"appropriate":[175],"filter":[176],"prove":[177],"energy-stability":[179],"remains":[180],"true":[181],"nonlinear":[185],"filter,":[186],"hence":[187],"displaying":[188],"some":[189],"robustness.":[190]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
