{"id":"https://openalex.org/W1533306886","doi":"https://doi.org/10.23919/ecc.2013.6669306","title":"On a time-varying stochastic small gain theorem","display_name":"On a time-varying stochastic small gain theorem","publication_year":2013,"publication_date":"2013-07-01","ids":{"openalex":"https://openalex.org/W1533306886","doi":"https://doi.org/10.23919/ecc.2013.6669306","mag":"1533306886"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.2013.6669306","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2013.6669306","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 European Control Conference (ECC)","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/A5037213683","display_name":"Samir Aberkane","orcid":"https://orcid.org/0000-0002-8657-6689"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]},{"id":"https://openalex.org/I4210164347","display_name":"Henri Poincar\u00e9 Institute","ror":null,"country_code":"FR","type":null,"lineage":["https://openalex.org/I4210164347"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"S. Aberkane","raw_affiliation_strings":["CRAN - CNRS UMR 7039, Universit\u00e9 Henri Poincar\u00e9, Nancy 1, France","CRAN, Univ. Henri Poincare, Vand\u0153uvre-le\u0300s-Nancy, France"],"affiliations":[{"raw_affiliation_string":"CRAN - CNRS UMR 7039, Universit\u00e9 Henri Poincar\u00e9, Nancy 1, France","institution_ids":["https://openalex.org/I4210164347","https://openalex.org/I90183372","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CRAN, Univ. Henri Poincare, Vand\u0153uvre-le\u0300s-Nancy, France","institution_ids":["https://openalex.org/I90183372"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038523391","display_name":"Vasile Dr\u01cegan","orcid":"https://orcid.org/0000-0001-6617-1441"},"institutions":[{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"V. Dragan","raw_affiliation_strings":["Institute of Mathematics of the Romanian Academy, Bucharest, Romania","\u201cSimion Stoilow\u201d Inst. of Math., Bucharest, Romania"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics of the Romanian Academy, Bucharest, Romania","institution_ids":["https://openalex.org/I58077936"]},{"raw_affiliation_string":"\u201cSimion Stoilow\u201d Inst. of Math., Bucharest, Romania","institution_ids":["https://openalex.org/I58077936"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5037213683"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210164347","https://openalex.org/I90183372"],"apc_list":null,"apc_paid":null,"fwci":0.505,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.69674656,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"81","last_page":"86"},"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":0.9991000294685364,"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":0.9991000294685364,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9919000267982483,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9918000102043152,"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/small-gain-theorem","display_name":"Small-gain theorem","score":0.6815895438194275},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.6215400099754333},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5991390943527222},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5743889212608337},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5336248278617859},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5164018273353577},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.5045598745346069},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.5021982192993164},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4630250036716461},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.4630034267902374},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4584720730781555},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.4551113545894623},{"id":"https://openalex.org/keywords/comparison-theorem","display_name":"Comparison theorem","score":0.4483656585216522},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.43288755416870117},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.42381802201271057},{"id":"https://openalex.org/keywords/argument","display_name":"Argument (complex analysis)","score":0.412384569644928},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.3011534810066223},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2888309359550476},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24589332938194275},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.22217810153961182},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.16920697689056396},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12612557411193848},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10716128349304199},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07604938745498657},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06734517216682434}],"concepts":[{"id":"https://openalex.org/C27385263","wikidata":"https://www.wikidata.org/wiki/Q4165677","display_name":"Small-gain theorem","level":3,"score":0.6815895438194275},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.6215400099754333},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5991390943527222},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5743889212608337},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5336248278617859},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5164018273353577},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.5045598745346069},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5021982192993164},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4630250036716461},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.4630034267902374},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4584720730781555},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.4551113545894623},{"id":"https://openalex.org/C2779396167","wikidata":"https://www.wikidata.org/wiki/Q5156040","display_name":"Comparison theorem","level":2,"score":0.4483656585216522},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.43288755416870117},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.42381802201271057},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.412384569644928},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3011534810066223},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2888309359550476},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24589332938194275},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.22217810153961182},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.16920697689056396},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12612557411193848},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10716128349304199},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07604938745498657},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06734517216682434},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/ecc.2013.6669306","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2013.6669306","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 European Control Conference (ECC)","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":8,"referenced_works":["https://openalex.org/W56139714","https://openalex.org/W1489051611","https://openalex.org/W1490978409","https://openalex.org/W1500134124","https://openalex.org/W1530564675","https://openalex.org/W1996927847","https://openalex.org/W2033951124","https://openalex.org/W2142482984"],"related_works":["https://openalex.org/W1980740683","https://openalex.org/W1987193149","https://openalex.org/W2037584720","https://openalex.org/W2043705677","https://openalex.org/W2126205885","https://openalex.org/W2097622270","https://openalex.org/W2620928602","https://openalex.org/W3102460617","https://openalex.org/W2093841944","https://openalex.org/W1990502710"],"abstract_inverted_index":{"In":[0],"this":[1],"note,":[2],"a":[3,10,36],"small":[4],"gain":[5],"result":[6,31],"is":[7,32],"presented":[8],"for":[9],"class":[11],"of":[12,25],"discrete-time":[13],"time-varying":[14],"Markovian":[15],"jump":[16],"systems":[17],"with":[18],"state-dependent":[19],"noise.":[20],"Using":[21],"the":[22,30],"stabilizing":[23],"solutions":[24],"some":[26],"generalized":[27],"Riccati":[28],"equations,":[29],"obtained":[33],"based":[34],"on":[35],"Lyapunov":[37],"type":[38],"argument.":[39]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
