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1、Automatica48(2012)2569–2576ContentslistsavailableatSciVerseScienceDirectAutomaticajournalhomepage:www.elsevier.com/locate/automaticaBriefpaper✩Stochasticinput-to-statestabilityofswitchedstochasticnonlinearsystemsPingZhaoa,1,WeiFengb,YuKangcaSchoolofElectricalEngineering,UniversityofJinan,J
2、inan250022,Shandong,ChinabCollegeofInformationSciencesandEngineering,ShandongAgriculturalUniversity,Taian271018,Shandong,ChinacDepartmentofAutomation,UniversityofScienceandTechnologyofChina,Hefei230026,Anhui,ChinaarticleinfoabstractArticlehistory:Inthispaper,globalasymptoticstabilityinprob
3、ability(GASiP)andstochasticinput-to-statestabilityReceived30August2011(SISS)fornonswitchedstochasticnonlinear(nSSNL)systemsandswitchedstochasticnonlinear(SSNL)Receivedinrevisedformsystemsareinvestigated.ForthestudyofGASiP,thedefinitionwhichweconsideredisnottheusual13March2012notionofasympt
4、oticstabilityinprobability(stabilityinprobabilityplusattractivityinprobability);itAccepted7May2012candepictthepropertiesofthesystemquantitatively.Correspondingly,basedonthisdefinition,someAvailableonline20July2012sufficientconditionsareprovidedfornSSNLsystemsandSSNLsystems.Furthermore,thed
5、efinitionofSISSisintroducedandcorrespondingcriteriaareprovidedfornSSNLsystemsandSSNLsystems.IntheKeywords:proofoftheaboveresults,toovercomethedifficultiescomingwiththeappearanceofswitchingandStochasticsystemsNonlinearsystemsthestochasticpropertyatthesametime,wegeneralizethepastcomparisonpr
6、incipleandfullyusetheSwitchedsystemspropertiesofthefunctionswhichweconstructed.Intermsoftheaveragedwell-timeoftheswitchingStochasticinput-to-statestabilitylaws,asufficientSISSconditionisobtainedforSSNLsystems.Finally,someexamplesareprovidedtoSISS-Lyapunovfunctiondemonstratetheapplicability
7、ofourresults.©2012ElsevierLtd.Allrightsreserved.1.Introductionareobtainedbymanyscholars,i.e.Sontag,WangandLin,etc.(Angeli,Sontag,&Wang,2000;Liberzon,Morse,&Sontag,2002;SincetheperformanceofarealcontrolsystemisaffectedmoreLin,Sontag,&Wang,1995,1996;Praly&Wang,1
