Exponential Stability of Impulsive Stochastic Delay Differential Systems

Abstract EN

This paper investigates the stability of stochastic delay differential systems with two kinds of impulses, that is, destabilizing impulses and stabilizing impulses.

Both the pth moment and almost sure exponential stability criteria are established by using the average impulsive interval.

When the impulses are regarded as disturbances, a lower bound of average impulsive interval is obtained; it means that the impulses should not happen too frequently.

On the other hand, when the impulses are used to stabilize the system, an upper bound of average impulsive interval is derived; namely, enough impulses are needed to stabilize the system.

The effectiveness of the proposed results is illustrated by two examples.