{"id":"https://openalex.org/W2340211353","doi":null,"title":"Ac onverse Lyapunov theorem for asymptotic stability in probability","display_name":"Ac onverse Lyapunov theorem for asymptotic stability in probability","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2340211353","mag":"2340211353"},"language":"en","primary_location":{"id":"mag:2340211353","doi":null,"is_oa":false,"landing_page_url":"https://www.ece.ucsb.edu/~hespanha/published/FP-12-136_01_MS.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5113632564","display_name":"Anantharaman Subbaraman","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Anantharaman Subbaraman","raw_affiliation_strings":["University of California Santa Barbara"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California Santa Barbara","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5113632564"],"corresponding_institution_ids":["https://openalex.org/I154570441"],"apc_list":null,"apc_paid":null,"fwci":1.5023,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.84099238,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":95},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"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":0.6093999743461609,"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":0.6093999743461609,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.08900000154972076,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.06199999898672104,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/converse-lyapunov-theorem","display_name":"converse Lyapunov theorem","score":0.9919999837875366},{"id":"https://openalex.org/keywords/asymptotic-stability-in-probability","display_name":"asymptotic stability in probability","score":0.9620000123977661},{"id":"https://openalex.org/keywords/discrete-time-stochastic-systems","display_name":"discrete-time stochastic systems","score":0.9890000224113464},{"id":"https://openalex.org/keywords/nonuniqueness-of-solutions","display_name":"non-uniqueness of solutions","score":0.9309999942779541},{"id":"https://openalex.org/keywords/set-valued-mappings","display_name":"set-valued mappings","score":0.9599999785423279},{"id":"https://openalex.org/keywords/global-asymptotic-stability","display_name":"global asymptotic stability","score":0.7369999885559082}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8082504272460938},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.805779218673706},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6441231966018677},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5736884474754333},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5721889734268188},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5167843103408813},{"id":"https://openalex.org/C37935115","wikidata":"https://www.wikidata.org/wiki/Q6707085","display_name":"Lyapunov redesign","level":4,"score":0.5108923316001892},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5056173801422119},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.48932474851608276},{"id":"https://openalex.org/C201030206","wikidata":"https://www.wikidata.org/wiki/Q5165805","display_name":"Control-Lyapunov function","level":5,"score":0.4415965676307678},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32536646723747253},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.13750779628753662},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.0759216845035553},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07332205772399902},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2340211353","doi":null,"is_oa":false,"landing_page_url":"https://www.ece.ucsb.edu/~hespanha/published/FP-12-136_01_MS.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W582868771","https://openalex.org/W1579485993","https://openalex.org/W1995713768","https://openalex.org/W1996327409","https://openalex.org/W2022181286","https://openalex.org/W2044741154","https://openalex.org/W2052873276","https://openalex.org/W2054136677","https://openalex.org/W2057820893","https://openalex.org/W2129792111","https://openalex.org/W2133841948","https://openalex.org/W2151136609","https://openalex.org/W2156188549","https://openalex.org/W2162807113","https://openalex.org/W2799137445"],"related_works":["https://openalex.org/W2012487366","https://openalex.org/W2060142034","https://openalex.org/W2097577241","https://openalex.org/W2162053828","https://openalex.org/W2156188549","https://openalex.org/W7096143153","https://openalex.org/W2165947763","https://openalex.org/W1996327409","https://openalex.org/W2070714351","https://openalex.org/W2134515699"],"abstract_inverted_index":{"Ac":[0],"onverse":[1],"Lyapunov":[2,52,83],"theorem":[3],"is":[4,37],"established":[5],"for":[6],"discrete-time":[7],"stochastic":[8],"systems":[9],"with":[10,85],"non-unique":[11],"solutions.":[12,65],"In":[13],"order":[14],"to":[15,80],"prove":[16],"the":[17,25,30,33,47,57,86],"result,":[18],"mild":[19],"regularity":[20,88],"conditions":[21],"are":[22,78],"imposed":[23],"on":[24,68],"set-valued":[26],"mapping":[27],"that":[28,59],"characterizes":[29],"update":[31],"of":[32,49,56,72],"system":[34],"state.":[35],"It":[36],"show":[38],"nt":[39],"hat":[40],"global":[41,73],"asymptotic":[42,74],"stability":[43,75],"in":[44,61,76],"probability":[45,77],"implies":[46],"existence":[48],"a":[50,82],"continuous":[51],"function,":[53],"smooth":[54],"outside":[55],"attractor,":[58],"decreases":[60],"expected":[62],"value":[63],"along":[64],"Additional":[66],"results":[67],"th":[69],"er":[70],"obustness":[71],"used":[79],"construct":[81],"function":[84],"desired":[87],"properties.":[89],"I.":[90],"INTRODUCTION":[91]},"counts_by_year":[{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T04:12:42.849631","created_date":"2016-06-24T00:00:00"}
