Stochastic ISS of Impulsive Evolution Equations with Randomly Distributed Jump Instants

This paper studies stochastic input-to-state stability of impulsive evolution equations with randomly distributed jump instants. We model these random jump instants via a Poisson process. Our approach derives the stability conditions by employing candidate Lyapunov functions parameterized by nonlinear rates. We apply our results to the cooling mechanism of a metal string modeled by a partial differential equation with jumps.