{"id":"https://openalex.org/W2165247181","doi":"https://doi.org/10.1109/acc.2006.1657447","title":"Best guaranteed bounds for simulations of nonlinear systems using linear Lyapunov-like functions","display_name":"Best guaranteed bounds for simulations of nonlinear systems using linear Lyapunov-like functions","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2165247181","doi":"https://doi.org/10.1109/acc.2006.1657447","mag":"2165247181"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2006.1657447","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2006.1657447","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 American Control Conference","raw_type":"proceedings-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/A5088168487","display_name":"Bernd Tibken","orcid":"https://orcid.org/0000-0002-4639-1487"},"institutions":[{"id":"https://openalex.org/I167360494","display_name":"University of Wuppertal","ror":"https://ror.org/00613ak93","country_code":"DE","type":"education","lineage":["https://openalex.org/I167360494"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"B. Tibken","raw_affiliation_strings":["Chair of Automatic Control, Faculty of Electrical, Information and Media Engineering, University of Wuppertal, Wuppertal, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Automatic Control, Faculty of Electrical, Information and Media Engineering, University of Wuppertal, Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034801721","display_name":"Marc Gennat","orcid":null},"institutions":[{"id":"https://openalex.org/I167360494","display_name":"University of Wuppertal","ror":"https://ror.org/00613ak93","country_code":"DE","type":"education","lineage":["https://openalex.org/I167360494"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"M. Gennat","raw_affiliation_strings":["Chair of Automatic Control, Faculty of Electrical, Information and Media Engineering, University of Wuppertal, Wuppertal, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Automatic Control, Faculty of Electrical, Information and Media Engineering, University of Wuppertal, Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I167360494"],"apc_list":null,"apc_paid":null,"fwci":0.3327,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.64429137,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"1","issue":null,"first_page":"6 pp.","last_page":"6 pp."},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9955999851226807,"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"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.7104911804199219},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.59906005859375},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5940194129943848},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5127476453781128},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5051830410957336},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.49624258279800415},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.49088674783706665},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.46864694356918335},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4538513422012329},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.44302403926849365},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4237968325614929},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.41658201813697815},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41591811180114746},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4135659635066986},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4029066264629364},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38508671522140503},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17632213234901428}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7104911804199219},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.59906005859375},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5940194129943848},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5127476453781128},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5051830410957336},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.49624258279800415},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.49088674783706665},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.46864694356918335},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4538513422012329},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44302403926849365},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4237968325614929},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.41658201813697815},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41591811180114746},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4135659635066986},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4029066264629364},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38508671522140503},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17632213234901428},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2006.1657447","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2006.1657447","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure","score":0.49000000953674316}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W268322338","https://openalex.org/W1531269771","https://openalex.org/W1985815049","https://openalex.org/W2014208555","https://openalex.org/W2036683060","https://openalex.org/W2060924166","https://openalex.org/W2067648572","https://openalex.org/W2085620496","https://openalex.org/W2117453669","https://openalex.org/W2129461175","https://openalex.org/W2317926736","https://openalex.org/W2328986487","https://openalex.org/W2483775066","https://openalex.org/W3004096462","https://openalex.org/W3146520007","https://openalex.org/W4206038828","https://openalex.org/W6659673746"],"related_works":["https://openalex.org/W2520934858","https://openalex.org/W2990487117","https://openalex.org/W2012882356","https://openalex.org/W109635080","https://openalex.org/W2377262226","https://openalex.org/W4285295794","https://openalex.org/W2098412892","https://openalex.org/W2531534085","https://openalex.org/W2387705642","https://openalex.org/W2372016227"],"abstract_inverted_index":{"The":[0,173,202],"models":[1],"of":[2,38,67,70,77,90,111,199],"biological":[3],"or":[4,18],"technical":[5],"applications":[6,46],"are":[7,23,47],"generally":[8],"represented":[9],"by":[10,59],"nonlinear":[11],"systems.":[12],"Moreover":[13],"these":[14,50],"systems":[15,71,79],"contain":[16],"uncertain":[17,113],"unknown":[19,92],"parameters.":[20,93,114],"These":[21],"uncertainties":[22,73],"reasons":[24],"for":[25,35,182],"some":[26,101],"numerical":[27,75],"and":[28,192,223],"analytical":[29],"problems":[30],"in":[31,53,100],"finding":[32],"guaranteed":[33,51,130,140,191],"bounds":[34,52,195],"the":[36,39,60,68,74,78,91,109,112,121,161,165,214,228],"solution":[37,69],"state":[40,61,215],"space":[41],"representation.":[42],"Unfortunately":[43],"several":[44,98],"industrial":[45,221],"demanding":[48],"exactly":[49],"order":[54],"to":[55,83,107,138,148,159,205,212],"fulfill":[56],"regulations":[57],"set":[58],"authorities.":[62],"To":[63],"get":[64,160],"an":[65,179,207,220],"idea":[66,203],"with":[72,86,167],"integration":[76],"differential":[80],"equations":[81],"has":[82],"be":[84,176],"done":[85,97],"random":[87],"selected":[88],"values":[89],"This":[94,115],"computation":[95],"is":[96,117,143,204],"times,":[99,106],"circumstances":[102],"more":[103],"than":[104],"thousand":[105],"cover":[108],"interval":[110,181,187],"approach":[116,127,166],"well":[118],"known":[119],"as":[120,178,196],"Monte-Carlo":[122],"method,":[123],"but":[124],"this":[125,150,153,157],"stochastic":[126],"cannot":[128],"deliver":[129],"bounds.":[131],"Thus,":[132],"we":[133,155],"developed":[134],"a":[135,197],"novel":[136],"method":[137,158],"find":[139,206],"bounds,":[141,163],"which":[142,164,210],"using":[144],"linear":[145,168],"Lyapunov-like":[146,169],"functions":[147,170],"solve":[149],"problem.":[151],"In":[152],"scope,":[154],"improved":[156],"best":[162],"can":[171,175],"provide.":[172],"results":[174,226],"used":[177],"initial":[180],"further":[183],"methods":[184],"based":[185],"on":[186],"arithmetic.":[188],"We":[189],"achieve":[190],"finite":[193],"simulation":[194,225],"result":[198],"our":[200],"approach.":[201],"auxiliary":[208],"function,":[209],"helps":[211],"bind":[213],"variables.":[216],"An":[217],"example":[218],"from":[219],"application":[222],"its":[224],"conclude":[227],"paper":[229]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
