{"id":"https://openalex.org/W2160033932","doi":"https://doi.org/10.1109/cdc.2007.4434827","title":"Connection between almost everywhere stability of an ODE and advection PDE","display_name":"Connection between almost everywhere stability of an ODE and advection PDE","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2160033932","doi":"https://doi.org/10.1109/cdc.2007.4434827","mag":"2160033932"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2007.4434827","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434827","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/A5062167831","display_name":"Rajeev Rajaram","orcid":"https://orcid.org/0000-0003-1680-6706"},"institutions":[{"id":"https://openalex.org/I107118585","display_name":"Shepherd University","ror":"https://ror.org/00y93ak93","country_code":"US","type":"education","lineage":["https://openalex.org/I107118585"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Rajeev Rajaram","raw_affiliation_strings":["Department of Computer Science, Mathematics and Engineering, Shepherd University, WV, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Mathematics and Engineering, Shepherd University, WV, USA","institution_ids":["https://openalex.org/I107118585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050749492","display_name":"Umesh Vaidya","orcid":"https://orcid.org/0000-0002-0483-4921"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Umesh Vaidya","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Iowa State University, IA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Iowa State University, IA, USA","institution_ids":["https://openalex.org/I173911158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057639149","display_name":"Makan Fardad","orcid":"https://orcid.org/0000-0003-4643-0535"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Makan Fardad","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Minnesota, MN, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Minnesota, MN, USA","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5062167831"],"corresponding_institution_ids":["https://openalex.org/I107118585"],"apc_list":null,"apc_paid":null,"fwci":0.7825,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.73848627,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"5880","last_page":"5885"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9983999729156494,"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"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9940000176429749,"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/almost-everywhere","display_name":"Almost everywhere","score":0.8933871984481812},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7091884613037109},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.6466635465621948},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5807874798774719},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.576814591884613},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5715667009353638},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5460957288742065},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5180683135986328},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5174946784973145},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5158021450042725},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5050914883613586},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.4427887201309204},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.436014324426651},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.42936956882476807},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3582555055618286},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.243495911359787},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1270865797996521},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0840880274772644},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.079424649477005},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.057469964027404785}],"concepts":[{"id":"https://openalex.org/C27142425","wikidata":"https://www.wikidata.org/wiki/Q1139334","display_name":"Almost everywhere","level":2,"score":0.8933871984481812},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7091884613037109},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.6466635465621948},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5807874798774719},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.576814591884613},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5715667009353638},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5460957288742065},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5180683135986328},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5174946784973145},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5158021450042725},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5050914883613586},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4427887201309204},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.436014324426651},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.42936956882476807},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3582555055618286},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.243495911359787},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1270865797996521},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0840880274772644},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.079424649477005},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.057469964027404785},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2007.4434827","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434827","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":10,"referenced_works":["https://openalex.org/W234899517","https://openalex.org/W1606157354","https://openalex.org/W2045938917","https://openalex.org/W2115805176","https://openalex.org/W2128629396","https://openalex.org/W2130415184","https://openalex.org/W2133330157","https://openalex.org/W2148780273","https://openalex.org/W2170665905","https://openalex.org/W2482944896"],"related_works":["https://openalex.org/W2371448224","https://openalex.org/W3134495997","https://openalex.org/W2363680170","https://openalex.org/W2130415184","https://openalex.org/W2780579194","https://openalex.org/W2054171707","https://openalex.org/W2128629396","https://openalex.org/W2161468807","https://openalex.org/W2291305206","https://openalex.org/W2526827983"],"abstract_inverted_index":{"A":[0],"result":[1],"on":[2],"the":[3,26,35,51,62],"necessary":[4],"and":[5],"sufficient":[6],"conditions":[7],"for":[8,68],"almost":[9,36],"everywhere":[10,37],"stability":[11,38],"of":[12,28,39,54,65],"an":[13,40],"invariant":[14,41],"set":[15],"in":[16],"continuous-time":[17],"dynamical":[18],"systems":[19],"is":[20,23,32],"presented.":[21],"It":[22],"shown":[24],"that":[25],"existence":[27],"a":[29,45,55],"Lyapunov":[30,66],"density":[31,46],"equivalent":[33],"to":[34,61],"set.":[42],"Furthermore,":[43],"such":[44],"can":[47],"be":[48],"obtained":[49],"as":[50],"positive":[52,63],"solution":[53,64],"linear":[56,70],"partial":[57],"differential":[58],"equation":[59,67],"analogous":[60],"stable":[69],"systems.":[71]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
