GKL‐finite‐time stability via comparison principles for stochastic impulsive systems.

This paper studies the finite‐time stability (FTS) for stochastic impulsive systems (SIS). The notions of FTS including GKL$$ \mathcal{GKL} $$‐FTS and event‐ GKL$$ \mathcal{GKL} $$‐FTS are proposed for SIS. The comparison principles for GKL$$ \mathcal{GKL} $$‐FTS and event‐ GKL$$ \mathcal{GKL} $$‐FTS are established, respectively. Then the FTS criteria with the settling time estimates are derived. The criteria of GKL$$ \mathcal{GKL} $$‐FTS and event‐ GKL$$ \mathcal{GKL} $$‐FTS relax the requirements on stabilizing flow and jump for FTS in the literature. Finally, two examples are presented to demonstrate the obtained results. [ABSTRACT FROM AUTHOR]