Studies on Controllability of Stochastic Impulsive Integrodifferential Systems in Hilbert Spaces

Abstract

Manystochasticimpulsivesystemsarisinginnatureexhibithereditaryproper­ties,thatis,state dependsonthepasttimehistory.Thetimehistory dependence ofstatesrenderstheequationsofmotionofstochasticimpulsivesystemsintheformofstochasticimpulsiveintegrodifferentialequations.Theresearchreportedinthisthesisdealswiththeproblemofcontrollabilityofnonlinearstochasticimpulsiveintegrodifferentialsystems.Theresultsareestablishedwithsuitableassumptionsonthenonlinearfunctions.Moreprecisely,wefirststudythecontrollabilityofthebasicstochasticintegrodifferentialsystemandextendedtheanalysistoageneralnonlinearproblemwithimpulsiveeffects.Thistechniquehasfurtherbeenappliedtotheproblemofcontrollabilityofstochasticimpulsivesystemswithmemoryinte­gralsandtime-varyingdelays.Further,wedealwiththecontrollabilityofsecondorderstochasticnonlinearimpulsivesystems.Inthiscontext,wehavefirstob­tainedthecontrollabilitytothesecondorderstochasticimpulsivesystemswiththeinitialconditions.Thenthesametechniquehassuccessfullybeenextendedwiththenonlocalconditions.Alltheresultsareobtainedbyusingthefixedpointtechniquesandthecontrollabilityofnonlinear stochasticimpulsivesystemsdependonthecontrollabilityresultsofanassociatedlinearstochasticimpulsivesystem.