In this paper, the $H_{\infty }$ 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 $H_{\infty }$ 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.

在本文中， $H_{\infty }$通过采用基于观测器的方法，针对一类具有信道衰落和随机变化的非线性（RVN）的不确定离散网络系统，讨论了滑模控制（SMC）问题。在这里，J采用三阶莱斯衰落模型来描述信道衰落现象，其中信道系数是相互独立的随机变量，它们以一定的间隔取值。另外，利用一系列相互独立的伯努利分布随机变量来表征RVN的现象，其中RVN的出现概率由名义均值和误差范围组成。解决的问题的主要目的是设计基于观察者的滑模控制器，以使闭环系统在均方意义上具有渐近稳定的特性，并且预先设定$H_{\infty }$性能要求得到保证。通过采用新颖的Lyapunov-Krasovskii泛函，可以得出足够的标准来迫使系统状态轨迹进入预先指定的滑模区域。然后，通过证明最小化问题的可行性，讨论了非凸问题的可解性。最后，给出一个说明性的例子来证明上述SMC技术的有效性。