{"id":"https://openalex.org/W2155689575","doi":"https://doi.org/10.1109/cdc.2008.4739402","title":"Non-monotonic Lyapunov functions for stability of discrete time nonlinear and switched systems","display_name":"Non-monotonic Lyapunov functions for stability of discrete time nonlinear and switched systems","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2155689575","doi":"https://doi.org/10.1109/cdc.2008.4739402","mag":"2155689575"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2008.4739402","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2008.4739402","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 47th 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/A5101485690","display_name":"Amir Ali Ahmadi","orcid":"https://orcid.org/0009-0001-5743-354X"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Amir Ali Ahmadi","raw_affiliation_strings":["Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, USA"],"affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031935416","display_name":"Pablo A. Parrilo","orcid":"https://orcid.org/0000-0003-1132-8477"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pablo A. Parrilo","raw_affiliation_strings":["Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, USA"],"affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101485690"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":9.0508,"has_fulltext":false,"cited_by_count":130,"citation_normalized_percentile":{"value":0.97659706,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"614","last_page":"621"},"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":0.9991000294685364,"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":0.9991000294685364,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9988999962806702,"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/T11236","display_name":"Control Systems and Identification","score":0.9959999918937683,"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/lyapunov-function","display_name":"Lyapunov function","score":0.7165820598602295},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6541194319725037},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.6195130944252014},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5796256065368652},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5750584006309509},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5097548365592957},{"id":"https://openalex.org/keywords/lyapunov-redesign","display_name":"Lyapunov redesign","score":0.5061141848564148},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5003089904785156},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.4851292073726654},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.4754473865032196},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.457184761762619},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.45452064275741577},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.40192803740501404},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3410169184207916},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.31264641880989075},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3105759620666504},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22038865089416504},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20314887166023254},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14038434624671936}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.7165820598602295},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6541194319725037},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6195130944252014},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5796256065368652},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5750584006309509},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5097548365592957},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.5061141848564148},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5003089904785156},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.4851292073726654},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.4754473865032196},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.457184761762619},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.45452064275741577},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.40192803740501404},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3410169184207916},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.31264641880989075},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3105759620666504},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22038865089416504},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20314887166023254},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14038434624671936},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2008.4739402","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2008.4739402","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 47th IEEE Conference on Decision and Control","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":28,"referenced_works":["https://openalex.org/W13975826","https://openalex.org/W1481077264","https://openalex.org/W1491672380","https://openalex.org/W1496537269","https://openalex.org/W1551193082","https://openalex.org/W1961645642","https://openalex.org/W1969174502","https://openalex.org/W1978242229","https://openalex.org/W1991656001","https://openalex.org/W2009668633","https://openalex.org/W2017888836","https://openalex.org/W2032326995","https://openalex.org/W2039434969","https://openalex.org/W2055472587","https://openalex.org/W2057209393","https://openalex.org/W2080688746","https://openalex.org/W2082419392","https://openalex.org/W2094426806","https://openalex.org/W2099212405","https://openalex.org/W2113789941","https://openalex.org/W2116816482","https://openalex.org/W2128506805","https://openalex.org/W2129492921","https://openalex.org/W2133404041","https://openalex.org/W3148663835","https://openalex.org/W3210839039","https://openalex.org/W4256127285","https://openalex.org/W6677229734"],"related_works":["https://openalex.org/W2349796700","https://openalex.org/W2284157877","https://openalex.org/W2383986032","https://openalex.org/W1789972284","https://openalex.org/W1983507234","https://openalex.org/W2534107666","https://openalex.org/W1986563546","https://openalex.org/W3194517843","https://openalex.org/W1979419366","https://openalex.org/W2411577087"],"abstract_inverted_index":{"We":[0,81,99],"relax":[1],"the":[2,10,35,64,101,142,172],"monotonicity":[3],"requirement":[4],"of":[5,12,18,103,116,133,144,162],"Lyapunov\u00bfs":[6],"theorem":[7],"to":[8,38,141],"enlarge":[9],"class":[11],"functions":[13,37,87,148],"that":[14,33,83,96,168],"can":[15,74,90,176],"provide":[16],"certificates":[17],"stability.":[19],"To":[20],"this":[21],"end,":[22],"we":[23,120,125,152],"propose":[24],"two":[25],"new":[26],"sufficient":[27],"conditions":[28],"for":[29],"global":[30],"asymptotic":[31],"stability":[32],"allow":[34],"Lyapunov":[36,86,108,147],"increase":[39],"locally,":[40],"but":[41,54],"guarantee":[42],"an":[43,56],"average":[44],"decrease":[45],"every":[46],"few":[47],"steps.":[48],"Our":[49],"first":[50,65],"condition":[51],"is":[52,71,137],"non-convex,":[53],"allows":[55],"intuitive":[57],"interpretation.":[58],"The":[59],"second":[60],"condition,":[61],"which":[62],"includes":[63],"one":[66,89],"as":[67,77],"a":[68,78,92,159],"special":[69],"case,":[70],"convex":[72],"and":[73],"be":[75,166,177],"cast":[76],"semidefinite":[79],"program.":[80],"show":[82],"when":[84],"non-monotonic":[85],"exist,":[88],"construct":[91],"more":[93],"complicated":[94],"function":[95],"decreases":[97],"monotonically.":[98],"demonstrate":[100],"strength":[102],"our":[104,180],"methodology":[105],"over":[106],"standard":[107],"theory":[109],"through":[110],"examples":[111],"from":[112,128],"three":[113],"different":[114],"classes":[115],"dynamical":[117],"systems.":[118],"First,":[119],"consider":[121],"polynomial":[122],"dynamics":[123],"where":[124],"utilize":[126],"techniques":[127],"sum-of-squares":[129],"programming.":[130],"Second,":[131],"analysis":[132],"piecewise":[134,145],"affine":[135],"systems":[136,154],"performed.":[138],"Here,":[139],"connections":[140],"method":[143],"quadratic":[146],"are":[149],"made.":[150],"Finally,":[151],"examine":[153],"with":[155],"arbitrary":[156],"switching":[157],"between":[158],"finite":[160],"set":[161],"matrices.":[163],"It":[164],"will":[165],"shown":[167],"tighter":[169],"bounds":[170],"on":[171],"joint":[173],"spectral":[174],"radius":[175],"obtained":[178],"using":[179],"technique.":[181]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":18},{"year":2019,"cited_by_count":17},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-01T08:55:55.761014","created_date":"2025-10-10T00:00:00"}
