New Relaxed Stability Conditions for Uncertain Two-Dimensional Discrete Systems

Abstract

This paper is concerned with the problem of robust stability of uncertain two-dimensional (2-D) discrete systems described by the Roesser model with polytopic uncertain parameters. Based on a newly developed parameter-dependent Lyapunov-Krasovski functional combined with Finsler's lemma, new sufficient conditions for robust stability analysis are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the effectiveness and less conservatism of the proposed results.

$$H_{\infty }$$ Model Reduction for 2-D Discrete Markovian Jump Systems

“…As is all known, many modern engineering fields, such as process control, transmission lines, image processing and signal filtering Du and Xie (2002), Kaczorek (1985), Lu (1992), have intrinsic 2-D characteristics, which motivates researchers to study the analysis and the design methods for 2-D systems. Accordingly, many problems on 2-D systems have been addressed; for example, stability and stabilization problems are studied in Badie et al (2018), Badie et al (2019), Tadepalli and Leite (2018), Yao et al (2013), control problem is investigated Badie et al (2020a), Duan and Xiang (2013), Fei et al (2017), Luo et al (2016) and filtering problem is discussed in Badie et al (2020b), Li and Gao (2013), Liang et al (2015), Xu et al (2017).…”

Reliable H∞ control for 2‐D discrete switched systems with state delays and actuator failures

“…2‐D systems can be described by various state‐space models such as the Rosser model, 6 Fornasini‐Marchesini (FM) model 7 and Attasi model 8 . Many results on 2‐D systems have been reported in the literature, to mention a few, the stability and stabilization of 2‐D systems have been solved in References 9‐12 and the H ∞ control and filtering problems have been investigated in References 13‐16.…”

H∞ Filtering for two-dimensional discrete switched systems in the second Fornasini and Marchesini model

“…Different from one-dimensional (1-D) systems, 2-D systems are a class of dynamic systems in which the information propagates along two independent directions, which make the study of those systems more complicated. However, many publications relating to the analysis and synthesis for 2-D systems have appeared; for example, the stability analysis problem for 2-D systems has been considered in Ahn et al (2016), Peng et al (2018) and Badie et al (2018a,b), and the control and filtering problems have been investigated in Xu and Zou (2010), Li and Gao (2013), Ghous and Xiang (2016) and Badie et al (2019a).…”