Non-Fragile H_∞ Deconvolution Filter Design for Uncertain Two-Dimensional Markovian Jump Systems With State-Varying Delays

Abstract

This paper addresses the problem of non-fragile $H_{\infty }$ deconvolution filtering for two-dimensional (2-D) Markovian jump systems with state-varying delays and norm-bounded uncertain terms. First, 2-D Markovian jump systems are modeled by using Fornasini-Marchesini (FM) model. Based on this system, a 2-D non-fragile $H_{\infty }$ deconvolution filter is designed. Second, by utilizing 2-D Lyapunov stability theory, stability criteria are derived to ensure that the filtering error system remains stochastically stable and satisfies the $H_{\infty }$ performance level $\gamma $ . Furthermore, sufficient conditions for the mode and delay dependence of the non-fragile $H_{\infty }$ deconvolution filter, as well as mode-dependent filter parameters, are achieved by using the linear matrix inequality (LMI) methods. Finally, the feasibility and effectiveness of the proposed non-fragile $H_{\infty }$ deconvolution filtering scheme are further demonstrated by an image denoising experiment.

Keywords

• Parameter uncertainties
• 2-D Markovian jump systems
• non-fragile H∞ deconvolution filter
• image denoising