H.Chen,L.Wang/AppliedMathematicsandComputation239(2014)320–325325
6
jd11jþ
ð1Àjd11jÞc21
and
2X
j¼1
2
c1Xa1jÀd1j
2j¼1
!2
2X32
þh1j<1;ð1Àjd11jÞc1j¼1
!2222XX6c2X32
jd22jþa2jÀd2jþh2j<1:ð1Àjd22jÞc2j¼12j¼1ð1Àjd22jÞc2j¼1
ItfollowsfromTheorem2thatregardlessofwhetherthetime-varyingdelayhðtÞisdifferentiableornot,thissystemsis
exponentiallystableinmeansquaremomentandalmostsurelyexponentiallystable.However,in[1–6,8–10,12,13,19,21],thecriteriacannotbeusedtoascertaintheexponentialstabilityinmeansquaremomentforsuchsystemwhenthederiv-ativevalueofthetime-varyingdelayfunctionhðtÞislargerthanoneandthetime-varyingdelayfunctionhðtÞisonlyrequiredtobeaboundedone.Fig.1illustratestheexponentialstabilityinmeansquaremomentandalmostsurelyexponentialsta-T
bilityofsuchsystemwhentheinitialvaluexðtÞ¼½0:01sinðtÞ;0:04cosðtÞ fort2½À10;0 .4.Conclusion
Inthispaper,theexponentialstabilityinmeansquaremomentforneutralstochasticsystemwithtime-varyingdelayhasbeendiscussedbyestablishinganintegralinequalityandutilizingthestochasticanalytictechnique.Andtheobtainedsta-bilitycriteriaarepresentedintermsofthealgebraicinequalities,whicharesuitableforthefasttime-varyingdelaycase.Finally,anillustrativenumericalexampleisgiventoshowtheeffectivenessoftheobtainedresults.Acknowledgement
Theauthorsareindebtedtotherefereesandtheeditorsfortheircarefullyreadingofthispaperandtheirvaluablecommentsandsuggestions.References
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