Observer-based SMC for stochastic systems with disturbance driven by fractional Brownian motion

This paper investigates the problem of disturbance-observer-based sliding mode control for stabilization of stochastic systems driven by fractional Brownian motion (fBm). By proposing a novel disturbance observer, an integral-type sliding surface is put forward with the estimated disturbance error confined within a certain value. Meanwhile, by virtue of fractional infinitesimal operator and linear matrix inequality, a sufficient criterion is derived to guarantee the asymptotic stability of obtained sliding mode dynamics. Further, an observer-based sliding mode controller is designed to ensure finite-time reachability of state trajectories onto the predefined sliding surface. Lastly, an illustrative example is utilized to verify the reliability and applicability of the proposed control strategy.