New Asymptotic Stability Conditions for Nonlinear Stochastic Systems Driven by Fractional Brownian Motion

Abstract

This paper is concerned with the asymptotic stability for nonlinear stochastic systems driven by fractional Brownian motion (fBm) with Hurst parameter H\in (1/2,1). First, some new asymptotic stability conditions are given for nonlinear stochastic systems with fBm by using the characteristic of the mild solution, the fBm, and the semigroup. Then, the results obtained are extended to the linear case, and some asymptotic stability conditions are derived. Furthermore, the methods proposed are utilized to solve the consensus control problem of the stochastic multi-agent systems (SMAS) with fBm. Finally, simulations are provided to illustrate the effectiveness of the proposed theoretical results.