Robust H∞ sliding mode control scheme for uncertain fractional stochastic systems: Nonlinear analysis and design

Abstract

This paper investigates the sliding mode control (SMC) design for fractional stochastic systems. We study a very general category of stochastic systems that are nonlinear and driven by fractional Brownian motion (fBm). A robust SMC scheme is presented for a fractional stochastic model with external disturbance, state‐ and disturbance‐dependent noise, and uncertainties, which ensures that the closed‐loop system is stochastically stable. We propose a novel sliding surface and then prove its reachability in the state space. Furthermore, the conditions for the stochastic stability of the sliding motion are derived via nonlinear Hamilton–Jacobi (HJ)‐type inequalities. In addition, an SMC method is developed for a special class of fractional stochastic models, and two sets of linear matrix inequality (LMI) conditions are obtained, which are sufficient for stochastic stability. Eventually, the validity of the results is validated via a simulation example.