Exponential stability of functional differential systems with impulsive effect on random moments (Q814104)

This paper is concerned with the \(p\)-moment exponential stability of the trivial solution of the following functional-differential systems with impulsive effect at random moments \[ x'(t)=f(t,x_{t}) \;a.e. \;t\in (\xi_{k-1},\xi_{k}), \;k=1,\dots, \] \[ \Delta x(\xi_{k})=I_{k}(\tau_{k},x(\xi_{k}^{-})), \;k=1,\dots, \] \[ x_{t_{0}}=\phi. \] The proof is based upon the Lyapunov direct method coupled with Razumikhin technique and a comparison principle. An example illustrates the applicability of the results proposed.