{"id":"https://openalex.org/W1544903188","doi":"https://doi.org/10.23919/ecc.1999.7100075","title":"Laguerre functions extended to any real derivative orders","display_name":"Laguerre functions extended to any real derivative orders","publication_year":1999,"publication_date":"1999-08-01","ids":{"openalex":"https://openalex.org/W1544903188","doi":"https://doi.org/10.23919/ecc.1999.7100075","mag":"1544903188"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.1999.7100075","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.1999.7100075","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1999 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/A5033566014","display_name":"Ludovic Le Lay","orcid":null},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ludovic Le Lay","raw_affiliation_strings":["Universite de Bordeaux, Talence, Aquitaine, FR","Equipe CRONE - LAP - ENSERB - Universit\u00e9 de Bordeaux I 351, cours de la Lib\u00e9ration - 33405 Talence cedex - France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universite de Bordeaux, Talence, Aquitaine, FR","institution_ids":["https://openalex.org/I15057530"]},{"raw_affiliation_string":"Equipe CRONE - LAP - ENSERB - Universit\u00e9 de Bordeaux I 351, cours de la Lib\u00e9ration - 33405 Talence cedex - France","institution_ids":["https://openalex.org/I15057530"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109881592","display_name":"Alain Oustaloup","orcid":null},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alain Oustaloup","raw_affiliation_strings":["Universite de Bordeaux, Talence, Aquitaine, FR","Equipe CRONE - LAP - ENSERB - Universit\u00e9 de Bordeaux I 351, cours de la Lib\u00e9ration - 33405 Talence cedex - France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universite de Bordeaux, Talence, Aquitaine, FR","institution_ids":["https://openalex.org/I15057530"]},{"raw_affiliation_string":"Equipe CRONE - LAP - ENSERB - Universit\u00e9 de Bordeaux I 351, cours de la Lib\u00e9ration - 33405 Talence cedex - France","institution_ids":["https://openalex.org/I15057530"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043987025","display_name":"Jocelyn Sabatier","orcid":"https://orcid.org/0000-0003-0085-7103"},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jocelyn Sabatier","raw_affiliation_strings":["Universite de Bordeaux, Talence, Aquitaine, FR","Equipe CRONE - LAP - ENSERB - Universit\u00e9 de Bordeaux I 351, cours de la Lib\u00e9ration - 33405 Talence cedex - France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universite de Bordeaux, Talence, Aquitaine, FR","institution_ids":["https://openalex.org/I15057530"]},{"raw_affiliation_string":"Equipe CRONE - LAP - ENSERB - Universit\u00e9 de Bordeaux I 351, cours de la Lib\u00e9ration - 33405 Talence cedex - France","institution_ids":["https://openalex.org/I15057530"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035293084","display_name":"Olivier Cois","orcid":null},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Olivier Cois","raw_affiliation_strings":["Universite de Bordeaux, Talence, Aquitaine, FR","Equipe CRONE - LAP - ENSERB - Universit\u00e9 de Bordeaux I 351, cours de la Lib\u00e9ration - 33405 Talence cedex - France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universite de Bordeaux, Talence, Aquitaine, FR","institution_ids":["https://openalex.org/I15057530"]},{"raw_affiliation_string":"Equipe CRONE - LAP - ENSERB - Universit\u00e9 de Bordeaux I 351, cours de la Lib\u00e9ration - 33405 Talence cedex - France","institution_ids":["https://openalex.org/I15057530"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I15057530"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"4686","last_page":"4691"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9997000098228455,"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/T11236","display_name":"Control Systems and Identification","score":0.9997000098228455,"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/T11081","display_name":"Advanced Control Systems Design","score":0.9927999973297119,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9872000217437744,"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/laguerre-polynomials","display_name":"Laguerre polynomials","score":0.9881154894828796},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.862633466720581},{"id":"https://openalex.org/keywords/laguerres-method","display_name":"Laguerre's method","score":0.7446260452270508},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6158385276794434},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5796211957931519},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5432291626930237},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5350723266601562},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5301856398582458},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.48745131492614746},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.468799889087677},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.43063831329345703},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32780951261520386},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3178136348724365},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2397877275943756},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.2129194140434265},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.1740986406803131},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1112731397151947},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06786459684371948}],"concepts":[{"id":"https://openalex.org/C108408018","wikidata":"https://www.wikidata.org/wiki/Q1124546","display_name":"Laguerre polynomials","level":2,"score":0.9881154894828796},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.862633466720581},{"id":"https://openalex.org/C43475892","wikidata":"https://www.wikidata.org/wiki/Q1171964","display_name":"Laguerre's method","level":4,"score":0.7446260452270508},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6158385276794434},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5796211957931519},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5432291626930237},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5350723266601562},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5301856398582458},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.48745131492614746},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.468799889087677},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.43063831329345703},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32780951261520386},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3178136348724365},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2397877275943756},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.2129194140434265},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.1740986406803131},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1112731397151947},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06786459684371948},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/ecc.1999.7100075","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.1999.7100075","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1999 European Control Conference (ECC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1553338987","https://openalex.org/W2055337535","https://openalex.org/W2142253184","https://openalex.org/W2161398593","https://openalex.org/W2561615412","https://openalex.org/W2564564625","https://openalex.org/W2571005040","https://openalex.org/W3038165843"],"related_works":["https://openalex.org/W1544903188","https://openalex.org/W2001654823","https://openalex.org/W2050355391","https://openalex.org/W1982489997","https://openalex.org/W2093444196","https://openalex.org/W2162397575","https://openalex.org/W2060075926","https://openalex.org/W2377100587","https://openalex.org/W2330120572","https://openalex.org/W2616692023"],"abstract_inverted_index":{"The":[0],"differentiation":[1],"orders":[2],"of":[3,20],"Laguerre":[4,7,42],"polynomials":[5],"and":[6,63],"functions":[8],"are":[9],"extended":[10],"to":[11,32,68],"permit":[12],"non":[13],"integer":[14,69],"values.":[15],"Using":[16],"this":[17],"new":[18],"class":[19],"functions,":[21],"a":[22],"complete":[23],"orthonormal":[24],"basis":[25,29],"is":[26,30],"constructed.":[27],"This":[28],"used":[31],"derive":[33],"an":[34,65],"identification":[35],"method":[36,50],"based":[37],"on":[38],"the":[39,49],"generalised":[40],"derivative":[41],"model.":[43],"An":[44],"academic":[45],"example":[46],"shows":[47],"that":[48],"can":[51],"provide":[52],"models":[53],"with":[54,59],"few":[55],"parameters":[56],"for":[57],"systems":[58],"distributed":[60],"time":[61],"constants,":[62],"thus":[64],"improvement":[66],"compared":[67],"order":[70],"models.":[71]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}