Robust Stabilization of Uncertain Time-Delay Systems With Fractional Stochastic Noise Using the Novel Fractional Stochastic Sliding Approach and Its Application to Stream Water Quality Regulation

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.