Fractional Brownian motion (fBm), known for its pronounced long-range dependence and persistent memory, poses substantial challenges to traditional stability analysis methods. To address these challenges, this paper investigates the asymptotic stability of discrete-time nonlinear stochastic systems driven by fBm with Hurst parameter \( H \in (\frac{1}{2}, 1) \) . By introducing an equivalent representation of fBm and exploiting its covariance structure, a new analytical framework is developed to handle the long-memory effect, thereby overcoming the main difficulty caused by the non-Markovian property of fBm. Based on this approach, a class of verifiable sufficient conditions for asymptotic stability is derived. The proposed results extend the classical stability theory of Brownian-driven systems to those affected by long-memory noise and provide new analytical tools for understanding their dynamic behavior. Numerical simulations are presented to confirm the correctness and applicability of the derived stability conditions.
