{"id":"https://openalex.org/W2041162749","doi":"https://doi.org/10.1109/tac.2013.2277620","title":"Equivalent Characterizations of Input-to-State Stability for Stochastic Discrete-Time Systems","display_name":"Equivalent Characterizations of Input-to-State Stability for Stochastic Discrete-Time Systems","publication_year":2013,"publication_date":"2013-08-07","ids":{"openalex":"https://openalex.org/W2041162749","doi":"https://doi.org/10.1109/tac.2013.2277620","mag":"2041162749"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2013.2277620","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2013.2277620","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-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","Electr. & Comput. Eng. Dept., Univ. of California Santa Barbara, Santa Barbara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Department, University of California, Santa Barbara, CA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Electr. & Comput. Eng. Dept., Univ. of California Santa Barbara, Santa Barbara, CA, 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. P. Hespanha","raw_affiliation_strings":["Electrical and Computer Engineering Department, University of California, Santa Barbara, CA","Electr. & Comput. Eng. Dept., Univ. of California Santa Barbara, Santa Barbara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Department, University of California, Santa Barbara, CA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Electr. & Comput. Eng. Dept., Univ. of California Santa Barbara, Santa Barbara, CA, 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","Electr. & Comput. Eng. Dept., Univ. of California Santa Barbara, Santa Barbara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Department, University of California, Santa Barbara, CA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Electr. & Comput. Eng. Dept., Univ. of California Santa Barbara, Santa Barbara, CA, 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":8.0793,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.97320515,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"59","issue":"2","first_page":"516","last_page":"522"},"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":0.9997000098228455,"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":0.9997000098228455,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9991999864578247,"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":0.9979000091552734,"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/mathematics","display_name":"Mathematics","score":0.7857759594917297},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5915902853012085},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5613359808921814},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.48822692036628723},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.44565582275390625},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.44182541966438293},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4380345344543457},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.43534421920776367},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4245093762874603},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10090738534927368},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09363409876823425}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7857759594917297},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5915902853012085},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5613359808921814},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.48822692036628723},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.44565582275390625},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.44182541966438293},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4380345344543457},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.43534421920776367},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4245093762874603},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10090738534927368},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09363409876823425},{"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},{"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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2013.2277620","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2013.2277620","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W2017493230","https://openalex.org/W2020711750","https://openalex.org/W2021469018","https://openalex.org/W2022181286","https://openalex.org/W2032633052","https://openalex.org/W2036826525","https://openalex.org/W2038137192","https://openalex.org/W2038874783","https://openalex.org/W2050693590","https://openalex.org/W2053860764","https://openalex.org/W2058243742","https://openalex.org/W2060142034","https://openalex.org/W2084729396","https://openalex.org/W2134078068","https://openalex.org/W2145015681","https://openalex.org/W2153392494","https://openalex.org/W2162053828","https://openalex.org/W2165626406","https://openalex.org/W3103012671","https://openalex.org/W4249513058"],"related_works":["https://openalex.org/W2164703465","https://openalex.org/W2168383058","https://openalex.org/W2143247663","https://openalex.org/W1965992231","https://openalex.org/W2050693590","https://openalex.org/W1990502710","https://openalex.org/W2159479095","https://openalex.org/W2095860056","https://openalex.org/W2351359734","https://openalex.org/W1603461487"],"abstract_inverted_index":{"Input-to-state":[0],"stability":[1,39,81],"(ISS)":[2],"for":[3,78],"stochastic":[4],"difference":[5],"inclusions":[6],"is":[7,18,31,52,94,97],"studied.":[8],"First,":[9],"ISS":[10,28,91],"in":[11,29,40,47,82,92],"probability":[12,30,41,83,93],"relative":[13],"to":[14,33,36,67,99],"a":[15,48,55,73],"compact":[16,69],"set":[17],"defined.":[19],"Subsequently,":[20],"several":[21],"equivalent":[22,35,86,102],"characterizations":[23],"are":[24],"given.":[25],"For":[26],"example,":[27],"shown":[32,98],"be":[34],"global":[37,79],"asymptotic":[38,80],"when":[42],"the":[43,62,65,68],"disturbance":[44],"takes":[45],"values":[46],"ball":[49],"whose":[50],"radius":[51],"determined":[53],"by":[54],"sufficiently":[56],"small,":[57],"but":[58],"unbounded,":[59],"function":[60],"of":[61,64],"distance":[63],"state":[66],"set.":[70],"In":[71],"turn,":[72],"recent":[74],"converse":[75],"Lyapunov":[76,87],"theorem":[77],"provides":[84],"an":[85],"characterization.":[88,103],"Finally,":[89],"robust":[90],"defined":[95],"and":[96],"give":[100],"another":[101]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}