This paper aims to solve the sliding mode control issue for the discrete nonlinear two-dimensional (2D) Fornasini–Marchesini second (FMII) model under the influence of quantisation error and stochastic packet loss. Firstly, an innovative stochastic 2D FMII sliding mode control model is constructed by considering quantisation error and Bernoulli packet loss process. And then we study the stability issue and formulate the corresponding stability criterion by virtue of the 2D sliding mode surface and a 2D sliding mode control law with data compensation. Subsequently, the reachability for the 2D sliding surface is verified by a innovative and executable 2D sliding mode control law. Besides, the article also formulates the adaptive intelligent iterative algorithms for the sliding mode surface gain and 2D sliding mode control algorithm, respectively. To conclude the paper, an example is provided to analyse its SMC problem under quantisation and stochastic packet loss. This example also shows the effectiveness of the theorems and algorithms proposed in this paper.

本文旨在解决离散非线性二维 (2D) Fornasini–Marchesini second (FMII) 模型在量化误差和随机丢包影响下的滑模控制问题。首先，通过考虑量化误差和伯努利丢包过程，构建了创新的随机二维FMII滑模控制模型。然后利用二维滑模面和带数据补偿的二维滑模控制律研究稳定性问题并制定相应的稳定性判据。随后，通过创新且可执行的二维滑模控制律验证二维滑动面的可达性。此外，本文还分别制定了滑模面增益的自适应智能迭代算法和二维滑模控制算法。在总结本文时，提供了一个例子来分析其在量化和随机丢包情况下的 SMC 问题。这个例子也展示了本文提出的定理和算法的有效性。