{"id":"https://openalex.org/W1535753971","doi":"https://doi.org/10.23919/ecc.2001.7075933","title":"Delay-independent small gain theorem and frequency domain interpretation of the Lyapunov-Krasovskii method for stability of nonlinear delay systems","display_name":"Delay-independent small gain theorem and frequency domain interpretation of the Lyapunov-Krasovskii method for stability of nonlinear delay systems","publication_year":2001,"publication_date":"2001-09-01","ids":{"openalex":"https://openalex.org/W1535753971","doi":"https://doi.org/10.23919/ecc.2001.7075933","mag":"1535753971"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.2001.7075933","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2001.7075933","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/A5072342207","display_name":"Pierre\u2010Alexandre Bliman","orcid":"https://orcid.org/0000-0002-7734-2928"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Pierre-Alexandre Bliman","raw_affiliation_strings":["I.N.R.I.A., Rocquencourt B.P. 105, 78153 Le Chesnay Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"I.N.R.I.A., Rocquencourt B.P. 105, 78153 Le Chesnay Cedex, France","institution_ids":["https://openalex.org/I1326498283"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5072342207"],"corresponding_institution_ids":["https://openalex.org/I1326498283"],"apc_list":null,"apc_paid":null,"fwci":5.2952,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.95744216,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"360","last_page":"365"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9993000030517578,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9993000030517578,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9984999895095825,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7090826630592346},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.6806056499481201},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6741830706596375},{"id":"https://openalex.org/keywords/small-gain-theorem","display_name":"Small-gain theorem","score":0.667941153049469},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6267791986465454},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.556357204914093},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.452526718378067},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.43201494216918945},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3858950138092041},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17301157116889954},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15737244486808777}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7090826630592346},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6806056499481201},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6741830706596375},{"id":"https://openalex.org/C27385263","wikidata":"https://www.wikidata.org/wiki/Q4165677","display_name":"Small-gain theorem","level":3,"score":0.667941153049469},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6267791986465454},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.556357204914093},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.452526718378067},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.43201494216918945},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3858950138092041},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17301157116889954},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15737244486808777},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/ecc.2001.7075933","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2001.7075933","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W38067576","https://openalex.org/W193977774","https://openalex.org/W1041597513","https://openalex.org/W1960635674","https://openalex.org/W1985155701","https://openalex.org/W2004470537","https://openalex.org/W2012150224","https://openalex.org/W2024713406","https://openalex.org/W2031088774","https://openalex.org/W2046874050","https://openalex.org/W2056912313","https://openalex.org/W2057999733","https://openalex.org/W2062412902","https://openalex.org/W2077418568","https://openalex.org/W2114251300","https://openalex.org/W2167640856","https://openalex.org/W2325390432","https://openalex.org/W2519872631","https://openalex.org/W3195133498","https://openalex.org/W3210839039"],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1097487277","https://openalex.org/W2768610039","https://openalex.org/W4308265086","https://openalex.org/W2949964783","https://openalex.org/W2801357573","https://openalex.org/W2106889256","https://openalex.org/W2982363256","https://openalex.org/W2974000959","https://openalex.org/W4281664580"],"abstract_inverted_index":{"The":[0,79],"purpose":[1],"of":[2,27,47,64,97],"this":[3,92],"note":[4],"is":[5,67,85,104],"to":[6,36,75,94],"study":[7],"the":[8,28,37,45,48,51,58,65,72,82,101],"relationship":[9],"between":[10,81],"a":[11,24],"certain":[12],"stability":[13],"criterion":[14],"for":[15,99],"nonlinear":[16],"delay":[17],"systems,":[18],"obtained":[19],"via":[20],"Lyapunov-Krasovskii":[21,102],"method,":[22],"and":[23],"delay-independent":[25],"version":[26],"small":[29],"gain":[30],"theorem.":[31],"We":[32],"show":[33],"that,":[34],"contrary":[35],"delay-free":[38],"case":[39],"(in":[40],"which":[41,100],"Kalman-Yakubovich-Popov":[42],"lemma":[43],"ensures":[44],"equivalence":[46],"two":[49,83],"approaches),":[50],"first":[52],"method":[53,103],"assumes":[54],"stronger":[55],"hypothesis":[56],"than":[57],"second":[59],"one.":[60],"However,":[61],"numerical":[62],"verification":[63],"former":[66],"in":[68],"general":[69],"NP-hard,":[70],"whereas":[71],"latter":[73],"leads":[74],"linear":[76],"matrix":[77],"inequalities.":[78],"difference":[80],"approaches":[84],"precisely":[86],"stated,":[87],"and,":[88],"among":[89],"other":[90],"benefits,":[91],"permits":[93],"exhibit":[95],"classes":[96],"problems":[98],"not":[105],"conservative.":[106]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}