H∞ deconvolution filter for two‐dimensional numerical systems using orthogonal moments

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.