LAUSR

In this paper, stochastic systems with fractional Gaussian noise (fGn) are stochastically stabilized using a new robust sliding mode control scheme. The system is assumed to have state time delay and the system matrices have uncertainties. The proposed sliding hyper-surface is a fractional Ito process which is proven to be attainable almost surely in finite time by applying the fractional Ito formula. The trajectories of the system will be kept within a time-varying region around the sliding hyper-surface. The stochastic asymptotic stability of the closed-loop dynamics at sliding mode is guaranteed by the feasibility of some linear matrix inequalities (LMIs). The usefulness of the theoretical findings is demonstrated by providing a case study on the problem of stream water quality standards regulation. In addition, to show the effectiveness and superiority of the method a numerical example is presented.