Research on almost sure exponential stability of jump-diffusion neutral stochastic differential delay systems

This article explored the almost sure exponential stability of the neutral stochastic differential delay system (JNSDDS, Equation (2)) with delay τ driven by both the Brownian motion and the Poisson process. It is showed that for each τ=τ0+τ¯ bounded by τ∗=τ0+τ¯∗>τ0, the JNSDDS (2) is almost surely exponentially stable, if the corresponding referenced neutral stochastic differential delay system (RJNSDDS, Equation (3)) with delay τ0 is almost surely exponentially stable. Moreover, an implicit upper bound for τ¯∗ can be ascertained numerically. Finally, explanatory examples are provided.