New result on exponential stability for neutral stochastic l

Newresultonexponentialstabilityforneutralstochasticlinearsystemwithtime-varyingdelay

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HuabinChen ,LiuWang

DepartmentofMathematics,SchoolofScience,NanchangUniversity,Nanchang330031,Jiangxi,PRChina

articleinfoabstract

Thispapermainlyconsiderstheproblemfortheexponentialstabilityofneutralstochasticlinearsystemwithtime-varyingdelay.Inthelightofacoupleddelay-integralinequalityandusingthestochasticanalytictechnique,theexponentialstabilitycriteriaforsuchsystemsaregivenintermofthealgebraicinequalities,regardlessofwhetherthetime-varyingdelayisdifferentiableornot.Anillustrativenumericalexampleisgiventoshowtheeffectivenessoftheobtainedresult.

Ó2014ElsevierInc.Allrightsreserved.

Keywords:

NeutralstochasticlinearsystemExponentialstability

AlmostsurelyexponentialstabilityTime-varyingdelay

1.Introduction

Neutralstochasticdelayedsystemhasbeenreceivedmuchattentionsinceneutralstochasticmodellingcanbeappliedintomanybranchesofscienceandengineering elds[13]andthereferencestherein.Theseapplicationsarelargelydependentuponthestabilityoftheequilibriumofsuchsystem,thatis,stabilityanalysisisoneofthemostcrucialpropertieswhentheyareappliedintosomerealisticproblems.Thestochastic lteringandcontrolproblemswithsystemmodelsexpressedbyneutralstochastictime-delaysystemwereconsideredin[2,3,8,21]andthereferencestherein.However,howtoseekthestabilitycriterionabouttheneutralstochasticdelayedsystemhasbecomeahotissue.In[7,13,23],theexponentialstabilityandthealmostsurelyexponentialstabilityforneutraldelayedstochasticneuralnetworkswasdiscussedbyusingtheRazumikhin-typetheoremandthesemi-martingaleconvergencetheorem,respectively,butthederivedcriteriain[7,13,23]areextremelydif culttobeveri ed.

Recently,thelinearmatrixinequality(LMI)isregardedasaprevalentapproachtodiscussthestabilityfordifferentialequationswithdelay.Byutilizingthefree-weightingmatrixtechniqueandtheboundingtechnique,someLMI-basedsuf -cientconditionsensuringtheexponentialstabilityinmeansquaremomentandH1controlforneuralstochastictime-delaysystemweregivenin[8];TheLMI-basedexponentialstabilitycriterionofsuchsystemswaspresentedbyestablishingthegeneralizedFinsler’sLemmain[9];In[19],theexponentialstabilityinmeansquaremomentforneutralstochastictime-delaysystemshavebeendiscussedbyusingthisusefulapproach.Andresortingtothemodetransformationmethodcoupledwiththetechniqueproposedin[11,14,15,17,18,20,22,24],theexponentialstabilityinmeansquaremomentforsuchsystemwasconsideredin[12].But,theconcernedproblemin[8–10,12]isonlyinvolvedwiththeconstant-delaycase.Recently,Balasubramaniametal.[1],Chenetal.[6],Dengetal.[10]andParketal.[16]havestudiedtherobustlystabilityforneutralstochasticneuralnetworkswithtime-varyingdelaywhenanadditionalrestrictiveconditionthatthederivativevalueofthe

ThisworkissupportedbytheNationalNaturalScienceFoundationofChinaunderGrantNo.61365013,andtheFoundationofJiangxiProvincialEducationsofChinaunderGrantNo.GJJ14155. Correspondingauthor.

E-mailaddress:chb_00721@http://www.77cn.com.cn(H.Chen).

http://www.77cn.com.cn/10.1016/j.amc.2014.04.047

0096-3003/Ó2014ElsevierInc.Allrightsreserved.

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