Global Finite-Time Stability for Stochastic Impulsive Systems via Comparison Approach

This paper studies the issue of finite-time stability (FTS) for stochastic impulsive systems (SIS). Based on the notion of FTS for deterministic impulsive systems in the literature, the FTS including global FTS (GFTS) is defined for SIS. By using the comparison principle of impulsive systems, two types of GFTS criteria for SIS are established. The first type of GFTS criteria requires both the flow and the jump to be stabilising for GFTS. And the settling-time is dependent on the initial state. The second type of GFTS criteria includes some state-dependent impulse conditions. From the second type of GFTS criteria, it only requires the jump to be stabilising for GFTS. And the settling-time is independent of the initial state. Finally, two examples with simulations are given to verify the effectiveness of the results.