Observer-based H∞ Sliding Mode Control for Networked Systems subject to Communication Channel Fading and Randomly Varying Nonlinearities

Abstract In this paper, the H ∞ sliding mode control (SMC) problem is discussed for a class of uncertain discrete networked systems with channel fading and randomly varying nonlinearities (RVNs) by employing the observer-based approach. Here, the Jth-order Rice fading model is adopted to describe the phenomenon of channel fading, where the channel coefficients are mutually independent random variables that take the values on certain interval. In addition, a sequence of mutually independent Bernoulli distributed random variables is utilized to characterize the phenomenon of the RVNs, where the occurrence probabilities of RVNs consist of the nominal mean and the bound of error. The main objective of the addressed problem is to design the observer-based sliding mode controller such that the closed-loop system is asymptotically stable in mean-square sense and the pre-specified H ∞ performance requirement is guaranteed. By employing novel Lyapunov-Krasovskii functional, sufficient criteria are derived to force the system state trajectories onto a pre-specified sliding mode region. Afterwards, the solvability of non-convex problem is discussed by testifying the feasibility of a minimization problem. Finally, an illustrative example is given to demonstrate the effectiveness of aforementioned SMC technique.