Stability analysis for stochastic impulsive system with brownian motion driven by quadratic variation

Abstract

In this paper, we aim to explore stochastic stability for nonlinear impulsive system with brownian motion driven by quadratic variation. The mathematical model of impulsive system is made up of differential form and quadratic variation by brownian motion which is independent of the impulsive of the system. Based on employing $\mathcal{L}$-operator, our proposed consequences supply sufficient conditions for $\gamma$-moment exponential stability when the impulsive of the system is deterministic. Finally, a practical example is performed to corroborate the benefits and validity of our theoretical analysis.