In this article, we propose the issue of H_∞ deconvolution filtering for two-dimensional (2D) systems described by the Fornasini–Marchesini local state-space model. The main challenge is the design of a deconvolution filter to rebuild the 2D signal so that the filter error system is asymptotically stable and preserves a guaranteed H_∞ performance. To overcome this issue, we use some free matrix variables to eliminate coupling between Lyapunov matrix and system matrices to obtain sufficient conditions in linear matrix inequality form to ensure the desired stability and performance of the error systems in the first time. Moreover, we use the orthogonal moments to extract the feature vectors to generate the input system, with the minimum information with and without noise. Simulation examples are provided to show that the new design technology proposed in this article achieves better H_∞ performance than the existing design methods. Finally, this work can be very helpful tools for the practitioners in telecommunication, and data scientists to aid them in deconvolution, diagnostic, and transmission.

中文翻译：

---

使用正交矩的二维数值系统的 H∞ 反卷积滤波器

在本文中，我们针对 Fornasini-Marchesini 局部状态空间模型描述的二维 (2D) 系统提出了H _∞反卷积滤波问题。主要挑战是设计去卷积滤波器来重建 2D 信号，以便滤波器误差系统渐近稳定并保持有保证的H _∞表现。为了克服这个问题，我们使用一些自由矩阵变量来消除李雅普诺夫矩阵与系统矩阵之间的耦合，以获得线性矩阵不等式形式的充分条件，从而在第一时间保证误差系统所需的稳定性和性能。此外，我们使用正交矩来提取特征向量以生成输入系统，具有带和不带噪声的最小信息。仿真实例表明本文提出的新设计技术比现有设计方法实现了更好的H _∞性能。最后，这项工作对于电信从业人员和数据科学家来说是非常有用的工具，可以帮助他们进行解卷积、诊断和传输。