Exponential stability of infinite-dimensional impulsive stochastic systems with Poisson jumps under aperiodically intermittent control.

This paper studies the problem of mean square exponential stability (ES) for a class of impulsive stochastic infinite-dimensional systems with Poisson jumps (ISIDSP) using aperiodically intermittent control (AIC). It provides a detailed analysis of impulsive disturbances, and the related inequalities are given for the two cases when the impulse perturbation occurs at the start time points of the control and rest intervals or non-startpoints, respectively. Additionally, in virtue of Yosida approximating systems, combining with the Lyapunov method, graph theory and the above inequalities, criteria for ES of the above impulsive stochastic infinite-dimensional systems are established under AIC for these two perturbation scenarios. These criteria elucidate the effects of the impulsive perturbation strength, the ratio of control period, to rest period, and network topology on ES. Finally, the theoretical results are applied to a class of neural networks with reaction-diffusion processes, and the effectiveness of the findings is validated through numerical simulations.