{"id":"https://openalex.org/W2121883859","doi":"https://doi.org/10.1109/cdc.2007.4434818","title":"Approximations of Lyapunov-Krasovskii functionals of complete type with given cross terms in the derivative for the stability of time delay systems","display_name":"Approximations of Lyapunov-Krasovskii functionals of complete type with given cross terms in the derivative for the stability of time delay systems","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2121883859","doi":"https://doi.org/10.1109/cdc.2007.4434818","mag":"2121883859"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2007.4434818","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434818","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","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/A5068787186","display_name":"B.M. Ochoa","orcid":"https://orcid.org/0000-0002-6985-4245"},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Center for Research and Advanced Studies of the National Polytechnic Institute","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"B. M. Ochoa","raw_affiliation_strings":["Department of Automatic Control, CINVESTAV, Mexico","CINVESTAV-IPN/Mexico"],"affiliations":[{"raw_affiliation_string":"Department of Automatic Control, CINVESTAV, Mexico","institution_ids":["https://openalex.org/I68368234"]},{"raw_affiliation_string":"CINVESTAV-IPN/Mexico","institution_ids":["https://openalex.org/I68368234"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043301628","display_name":"Sabine Mondi\u00e9","orcid":"https://orcid.org/0000-0002-0968-1899"},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Center for Research and Advanced Studies of the National Polytechnic Institute","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"S. Mondie","raw_affiliation_strings":["Department of Automatic Control, CINVESTAV, Mexico","CINVESTAV-IPN/Mexico"],"affiliations":[{"raw_affiliation_string":"Department of Automatic Control, CINVESTAV, Mexico","institution_ids":["https://openalex.org/I68368234"]},{"raw_affiliation_string":"CINVESTAV-IPN/Mexico","institution_ids":["https://openalex.org/I68368234"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068787186"],"corresponding_institution_ids":["https://openalex.org/I68368234"],"apc_list":null,"apc_paid":null,"fwci":4.3547,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.94400595,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"99","issue":null,"first_page":"2071","last_page":"2076"},"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":0.989799976348877,"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":0.989799976348877,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9842000007629395,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9641000032424927,"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/constructive","display_name":"Constructive","score":0.7492936849594116},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7485198378562927},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6548628211021423},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5963619947433472},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5421465635299683},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5404146909713745},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4891229271888733},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47756391763687134},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4703417420387268},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.448012113571167},{"id":"https://openalex.org/keywords/stability-conditions","display_name":"Stability conditions","score":0.44728323817253113},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.42113468050956726},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.41252946853637695},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38819462060928345},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3782336711883545},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2688805162906647},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1380995213985443},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.09139886498451233}],"concepts":[{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.7492936849594116},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7485198378562927},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6548628211021423},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5963619947433472},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5421465635299683},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5404146909713745},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4891229271888733},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47756391763687134},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4703417420387268},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.448012113571167},{"id":"https://openalex.org/C143170015","wikidata":"https://www.wikidata.org/wiki/Q17007850","display_name":"Stability conditions","level":3,"score":0.44728323817253113},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.42113468050956726},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.41252946853637695},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38819462060928345},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3782336711883545},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2688805162906647},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1380995213985443},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.09139886498451233},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2007.4434818","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434818","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W116783994","https://openalex.org/W1607633954","https://openalex.org/W1981140738","https://openalex.org/W2014172170","https://openalex.org/W2015615314","https://openalex.org/W2047505817","https://openalex.org/W2051079365","https://openalex.org/W2072840336","https://openalex.org/W2110175274","https://openalex.org/W2113467155","https://openalex.org/W4211202937","https://openalex.org/W4293087381"],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W2383986032","https://openalex.org/W2534107666","https://openalex.org/W3194517843","https://openalex.org/W2121515234","https://openalex.org/W1977987201","https://openalex.org/W2059628530","https://openalex.org/W2210722882","https://openalex.org/W4387674644","https://openalex.org/W2032242696"],"abstract_inverted_index":{"Sufficient":[0],"conditions":[1,35],"expressed":[2],"in":[3,65],"terms":[4],"of":[5,10,14,27],"the":[6,11,15,20,24,28,57],"piecewise":[7],"linear":[8],"approximation":[9,49],"Lyapunov":[12,45],"matrix":[13,46],"time":[16],"delay":[17],"system":[18],"for":[19],"derivative":[21],"condition":[22,26],"and":[23],"bound":[25],"Lyapunov-Krasovskii":[29,58],"stability":[30],"Theorem":[31],"are":[32],"provided.":[33],"These":[34],"can":[36,61],"be":[37,63],"utilized":[38],"to":[39,52],"verify":[40],"if":[41],"a":[42,53,66],"given":[43],"constructed":[44],"or":[47],"its":[48],"gives":[50],"rise":[51],"functional":[54],"that":[55],"satisfies":[56],"theorem.":[59],"They":[60],"also":[62],"employed":[64],"constructive":[67],"manner.":[68]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}