LAUSR

Abstract In this paper, a class of linear stochastic systems driven by fractional Brownian motion are investigated. The fractional infinitesimal operator and stability criterion based on the Lyapunov approach for the systems with fractional stochastic noise are employed, which are different from the results of classical stochastic systems. Firstly, the robust H ∞ filtering problem is studied, and the stochastic stability and H ∞ performance of the filtering error system are guaranteed by the feasibility of linear matrix inequalities. Secondly, robust H ∞ control problem is investigated, and the closed-loop system driven by a fractional Brownian motion is stochastically stable and has H ∞ performance if some linear matrix inequalities are feasible under the designed controller. Finally, two numerical examples show the effectiveness and correctness of the proposed methods.