{"id":"https://openalex.org/W2089073842","doi":"https://doi.org/10.1109/cdc.2012.6425860","title":"Stochastic difference inclusions: Results on recurrence and asymptotic stability in probability","display_name":"Stochastic difference inclusions: Results on recurrence and asymptotic stability in probability","publication_year":2012,"publication_date":"2012-12-01","ids":{"openalex":"https://openalex.org/W2089073842","doi":"https://doi.org/10.1109/cdc.2012.6425860","mag":"2089073842"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2012.6425860","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2012.6425860","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE 51st IEEE Conference on Decision and Control (CDC)","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/A5002737786","display_name":"Andrew R. Teel","orcid":"https://orcid.org/0000-0002-6508-0879"},"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":"A.R. Teel","raw_affiliation_strings":["Electrical and Computer Engineering Department, University of California, Santa Barbara, CA, USA","Electrical and Computer Engineering Department, University of California Santa Barbara, 93106-9560, USA"],"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Department, University of California, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Electrical and Computer Engineering Department, University of California Santa Barbara, 93106-9560, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065218317","display_name":"Jo\u00e3o P. Hespanha","orcid":"https://orcid.org/0000-0003-2809-4718"},"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":false,"raw_author_name":"J. Hespanha","raw_affiliation_strings":["Electrical and Computer Engineering Department, University of California, Santa Barbara, CA, USA","Electrical and Computer Engineering Department, University of California Santa Barbara, 93106-9560, USA"],"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Department, University of California, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Electrical and Computer Engineering Department, University of California Santa Barbara, 93106-9560, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113632564","display_name":"Anantharaman Subbaraman","orcid":null},"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":false,"raw_author_name":"A. Subbaraman","raw_affiliation_strings":["Electrical and Computer Engineering Department, University of California, Santa Barbara, CA, USA","Electrical and Computer Engineering Department, University of California Santa Barbara, 93106-9560, USA"],"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Department, University of California, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Electrical and Computer Engineering Department, University of California Santa Barbara, 93106-9560, USA","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5002737786"],"corresponding_institution_ids":["https://openalex.org/I154570441"],"apc_list":null,"apc_paid":null,"fwci":2.2522,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.89505104,"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":"4051","last_page":"4056"},"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":0.9987999796867371,"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":0.9987999796867371,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9970999956130981,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5940704345703125},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5557507276535034},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4582710564136505},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4375561475753784},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42228594422340393},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.15570324659347534},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.1305476725101471},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.084622323513031}],"concepts":[{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5940704345703125},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5557507276535034},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4582710564136505},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4375561475753784},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42228594422340393},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.15570324659347534},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.1305476725101471},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.084622323513031},{"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.2012.6425860","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2012.6425860","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE 51st IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5699999928474426,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1540519426","https://openalex.org/W1579485993","https://openalex.org/W1900371862","https://openalex.org/W1983176609","https://openalex.org/W1995713768","https://openalex.org/W2004299821","https://openalex.org/W2022181286","https://openalex.org/W2028194350","https://openalex.org/W2041162749","https://openalex.org/W2044741154","https://openalex.org/W2057820893","https://openalex.org/W2060142034","https://openalex.org/W2076337359","https://openalex.org/W2084828843","https://openalex.org/W2095907778","https://openalex.org/W2099308299","https://openalex.org/W2112248103","https://openalex.org/W2134078068","https://openalex.org/W2142518629","https://openalex.org/W2145415070","https://openalex.org/W2146851017","https://openalex.org/W2170882877","https://openalex.org/W2327622497","https://openalex.org/W2340211353","https://openalex.org/W2488096466","https://openalex.org/W2607614170","https://openalex.org/W4212875940","https://openalex.org/W4235816940","https://openalex.org/W4244560419","https://openalex.org/W4249513058","https://openalex.org/W4290744580","https://openalex.org/W4301524229","https://openalex.org/W6639670352"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596"],"abstract_inverted_index":{"Stability":[0],"theory":[1,29],"for":[2,12,22],"stochastic":[3,13],"difference":[4,14],"inclusions":[5,15],"is":[6],"discussed.":[7],"We":[8,61],"summarize":[9],"a":[10,24],"framework":[11,74],"that":[16],"has":[17],"been":[18,32],"introduced":[19],"recently":[20],"and":[21,39,57,75],"which":[23],"variety":[25],"of":[26],"new":[27,50],"stability":[28,42,65],"results":[30,51],"have":[31],"obtained.":[33],"In":[34],"particular,":[35],"we":[36,48],"study":[37],"recurrence":[38],"global":[40],"asymptotic":[41],"in":[43,66],"probability.":[44,67],"For":[45],"these":[46],"properties,":[47],"review":[49],"on":[52],"robustness,":[53],"converse":[54],"Lyapunov":[55],"theorems,":[56],"Matrosov-function-based":[58],"sufficient":[59],"conditions.":[60],"also":[62],"discuss":[63],"input-to-state":[64],"Examples":[68],"are":[69],"used":[70],"to":[71],"illustrate":[72],"the":[73],"results.":[76]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}