{"id":"https://openalex.org/W1542226507","doi":"https://doi.org/10.1109/cdc.2003.1272442","title":"Converse theorems of the principal Lyapunov results for partial stability of general dynamical systems on metric spaces","display_name":"Converse theorems of the principal Lyapunov results for partial stability of general dynamical systems on metric spaces","publication_year":2004,"publication_date":"2004-06-03","ids":{"openalex":"https://openalex.org/W1542226507","doi":"https://doi.org/10.1109/cdc.2003.1272442","mag":"1542226507"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2003.1272442","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2003.1272442","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)","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/A5049259288","display_name":"A. P. Molchanov","orcid":"https://orcid.org/0000-0003-2133-247X"},"institutions":[{"id":"https://openalex.org/I4210157430","display_name":"V. A. Trapeznikov Institute of Control Sciences","ror":"https://ror.org/05f3yt521","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210157430","https://openalex.org/I4210164537"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"A.P. Molchanov","raw_affiliation_strings":["Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia","institution_ids":["https://openalex.org/I4210157430"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046850315","display_name":"A.N. Michel","orcid":null},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A.N. Michel","raw_affiliation_strings":["Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100713886","display_name":"Yan Sun","orcid":"https://orcid.org/0000-0003-2320-8245"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Y. Sun","raw_affiliation_strings":["Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4242,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.53816605,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"5085","last_page":"5090"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.984000027179718,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.984000027179718,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T13234","display_name":"advanced mathematical theories","score":0.9617000222206116,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9563000202178955,"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/converse","display_name":"Converse","score":0.9441635608673096},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7288368940353394},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.6483891606330872},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.615589439868927},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6004185676574707},{"id":"https://openalex.org/keywords/principal","display_name":"Principal (computer security)","score":0.5157599449157715},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5146142244338989},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5096089839935303},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.48454275727272034},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4733959436416626},{"id":"https://openalex.org/keywords/principal-part","display_name":"Principal part","score":0.46924734115600586},{"id":"https://openalex.org/keywords/converse-theorem","display_name":"Converse theorem","score":0.4346403479576111},{"id":"https://openalex.org/keywords/lyapunov-stability","display_name":"Lyapunov stability","score":0.41539761424064636},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41350606083869934},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41266512870788574},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.15811607241630554},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12033870816230774},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10083416104316711}],"concepts":[{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.9441635608673096},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7288368940353394},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.6483891606330872},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.615589439868927},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6004185676574707},{"id":"https://openalex.org/C144559511","wikidata":"https://www.wikidata.org/wiki/Q2986279","display_name":"Principal (computer security)","level":2,"score":0.5157599449157715},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5146142244338989},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5096089839935303},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.48454275727272034},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4733959436416626},{"id":"https://openalex.org/C194053038","wikidata":"https://www.wikidata.org/wiki/Q7245087","display_name":"Principal part","level":2,"score":0.46924734115600586},{"id":"https://openalex.org/C204591131","wikidata":"https://www.wikidata.org/wiki/Q5166461","display_name":"Converse theorem","level":3,"score":0.4346403479576111},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.41539761424064636},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41350606083869934},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41266512870788574},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.15811607241630554},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12033870816230774},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10083416104316711},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C132817261","wikidata":"https://www.wikidata.org/wiki/Q1134435","display_name":"Automorphic form","level":2,"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/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2003.1272442","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2003.1272442","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)","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":13,"referenced_works":["https://openalex.org/W139134227","https://openalex.org/W582868771","https://openalex.org/W1527177198","https://openalex.org/W1542226507","https://openalex.org/W1566074749","https://openalex.org/W2030148719","https://openalex.org/W2040601125","https://openalex.org/W2063818274","https://openalex.org/W2077719200","https://openalex.org/W2166856345","https://openalex.org/W2329719292","https://openalex.org/W2495048106","https://openalex.org/W4254127125"],"related_works":["https://openalex.org/W2144181412","https://openalex.org/W4394651134","https://openalex.org/W3033882599","https://openalex.org/W2136333882","https://openalex.org/W2342098551","https://openalex.org/W2990876408","https://openalex.org/W2975771407","https://openalex.org/W1986206926","https://openalex.org/W2910215732","https://openalex.org/W1984199859"],"abstract_inverted_index":{"We":[0,21],"present":[1],"converse":[2],"theorems":[3],"for":[4],"the":[5,23,37,49],"principal":[6],"Lyapunov":[7],"results":[8],"concerning":[9],"partial":[10,27],"stability":[11,28],"properties":[12],"of":[13,26,36,51],"general":[14,24],"dynamical":[15],"systems":[16],"defined":[17],"on":[18],"metric":[19],"spaces.":[20],"consider":[22],"case":[25,50],"(y-stability)":[29],"with":[30],"respect":[31],"to":[32],"disturbances":[33],"in":[34],"all":[35],"initial":[38],"state":[39],"variables":[40],"x/sub":[41],"0/=(y/sub":[42],"0/,":[43],"z/sub":[44],"0/)":[45],"as":[46,48],"well":[47],"y-stability":[52],"under":[53],"arbitrary":[54],"z-perturbations.":[55]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
