{"id":"https://openalex.org/W2007596781","doi":"https://doi.org/10.1109/cdc.2008.4738705","title":"Finite-time and practical stability of a class of stochastic dynamical systems","display_name":"Finite-time and practical stability of a class of stochastic dynamical systems","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2007596781","doi":"https://doi.org/10.1109/cdc.2008.4738705","mag":"2007596781"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2008.4738705","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2008.4738705","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 47th 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/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":true,"raw_author_name":"Anthony N. Michel","raw_affiliation_strings":["Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA","[Dept. of Electr. Eng., Univ. of Notre Dame, Notre Dame, IN, USA]"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"[Dept. of Electr. Eng., Univ. of Notre Dame, Notre Dame, IN, USA]","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101754282","display_name":"Ling Hou","orcid":"https://orcid.org/0000-0001-7070-1492"},"institutions":[{"id":"https://openalex.org/I173963315","display_name":"St. Cloud State University","ror":"https://ror.org/016czhx14","country_code":"US","type":"education","lineage":["https://openalex.org/I173963315","https://openalex.org/I91221267"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ling Hou","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Saint Cloud State University, Saint Cloud, MN, USA","Dept. of Electr. & Comput. Eng., St. Cloud State Univ., St. Cloud, MN, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Saint Cloud State University, Saint Cloud, MN, USA","institution_ids":["https://openalex.org/I173963315"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng., St. Cloud State Univ., St. Cloud, MN, USA","institution_ids":["https://openalex.org/I173963315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046850315"],"corresponding_institution_ids":["https://openalex.org/I107639228"],"apc_list":null,"apc_paid":null,"fwci":4.1125,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.93408205,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"3452","last_page":"3456"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9984999895095825,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9984999895095825,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9954000115394592,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.994700014591217,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.7717210054397583},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.722903847694397},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.6546002626419067},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6153691411018372},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5604316592216492},{"id":"https://openalex.org/keywords/stability-theory","display_name":"Stability theory","score":0.5572884678840637},{"id":"https://openalex.org/keywords/lyapunov-stability","display_name":"Lyapunov stability","score":0.5373085737228394},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.522232174873352},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.513202428817749},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5064648389816284},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.43823832273483276},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.41869622468948364},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.4150660037994385},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35919952392578125},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22923094034194946},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.17640414834022522},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.13665497303009033},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06364744901657104},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05667304992675781}],"concepts":[{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.7717210054397583},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.722903847694397},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.6546002626419067},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6153691411018372},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5604316592216492},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.5572884678840637},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.5373085737228394},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.522232174873352},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.513202428817749},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5064648389816284},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.43823832273483276},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.41869622468948364},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.4150660037994385},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35919952392578125},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22923094034194946},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.17640414834022522},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.13665497303009033},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06364744901657104},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05667304992675781},{"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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2008.4738705","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2008.4738705","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 47th IEEE Conference on Decision and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1489872560","https://openalex.org/W1527177198","https://openalex.org/W1536904835","https://openalex.org/W1568674094","https://openalex.org/W1983097489","https://openalex.org/W2005994183","https://openalex.org/W2049371567","https://openalex.org/W2071520194","https://openalex.org/W2100708180","https://openalex.org/W2106227786","https://openalex.org/W2160469521","https://openalex.org/W2480700567","https://openalex.org/W3022150416","https://openalex.org/W4254127125","https://openalex.org/W6628774300"],"related_works":["https://openalex.org/W2106591639","https://openalex.org/W2383820201","https://openalex.org/W2054744054","https://openalex.org/W1493913984","https://openalex.org/W2017132685","https://openalex.org/W3195658147","https://openalex.org/W2107865960","https://openalex.org/W2056331048","https://openalex.org/W2073181848","https://openalex.org/W2389586103"],"abstract_inverted_index":{"In":[0,55],"practice,":[1],"one":[2],"is":[3],"not":[4],"only":[5],"interested":[6],"in":[7,18,42,103,107],"qualitative":[8],"characterizations":[9],"provided":[10],"by":[11,76,84,118],"Lyapunov":[12],"and":[13,31,52,67,100,106],"Lagrange":[14],"stability,":[15],"but":[16],"also":[17],"quantitative":[19],"information":[20,38],"concerning":[21],"system":[22],"behavior,":[23],"including":[24],"estimates":[25],"of":[26,37,49,62,88,96,115,120],"trajectory":[27],"bounds":[28],"over":[29],"finite":[30],"infinite":[32],"time":[33],"intervals.":[34],"This":[35],"type":[36],"has":[39],"been":[40],"ascertained":[41],"a":[43],"systematic":[44],"manner":[45],"using":[46],"the":[47,56,63,104,108,113],"notions":[48],"finite-time":[50,65,99],"stability":[51,66,69,97,102],"practical":[53,68,101],"stability.":[54],"present":[57],"paper":[58],"we":[59],"generalize":[60],"some":[61],"existing":[64],"results":[70,117],"for":[71],"deterministic":[72],"dynamical":[73,81],"systems":[74,82],"determined":[75,83],"ordinary":[77],"differential":[78,90],"equations":[79],"to":[80],"an":[85],"important":[86],"class":[87],"stochastic":[89],"equations.":[91],"We":[92,111],"consider":[93],"two":[94],"types":[95],"concepts:":[98],"mean":[105,109],"square.":[110],"demonstrate":[112],"applicability":[114],"our":[116],"means":[119],"several":[121],"examples.":[122]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}