Finite-time stability of stochastic systems driven by fractional Brownian motion

Finite-time stability (FTS) is crucial for modern engineering systems with stringent real-time requirements. This paper investigates FTS for stochastic nonlinear systems driven by fractional Brownian motion (fBm), a process exhibiting long-range dependence. The non-semimartingale property of fBm presents analytical challenges. Utilizing fractional Wick-Itô-Skorohod integrals and the fractional Itô formula, the finite-time dynamics are rigorously analyzed. It is demonstrated that FTS cannot be achieved under Lipschitz conditions. Sufficient conditions for FTS are established, and an explicit estimate of the settling time is provided. Numerical simulations validate the theoretical results.