A Novel Approach to Delay-Variation-Dependent Stability Analysis of 2-D Discrete-Time Systems With Mixed Delays

Abstract

In this paper, a stability analysis problem is studied for a class of two-dimensional (2-D) discrete-time systems with time-varying and distributed delays described by the second Fornasini-Marchesini (FM) model. First, new 2-D polynomials-based summation inequalities are proposed to estimate summation terms in the forward difference of Lyapunov-Krasovskii functional (LKF). The inequalities can reduce to 2-D Jensen inequalities and 2-Dfinite-sum inequalities by designing slack matrices and arbitrary vectors. Second, a new augment LKF is constructed, which makes full use of the delay changing information. By the Lyapunov stability theory, sufficient conditions for asymptotic stability of 2-D discrete-time systems are derived in the form of linear matrix inequalities. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed methods. INDEX TERMS Two-dimensional systems, time-varying delays, distributed delays, summation inequalities, Lyapunov-Krasovskii functional.

Event-triggered control of switched 2D continuous-discrete systems

“… H ∞ controllers and H ∞ filters for 2D continuous systems were designed in the literature (Duan and Xiang, 2017; El-Amrani et al, 2018; Khald et al, 2020). There are also lots of important results on stability and control design of 2D discrete systems available in the literature (Hanba, 2020; Hua et al, 2018; Khald et al, 2019; Peng and Xu, 2019; Yang et al, 2020; Zhao et al, 2019). To name a few, Peng and Xu (2019) proposed a robust H ∞ filtering algorithm for 2D linear uncertain time-varying systems.…”

“…There are also lots of important results on stability and control design of 2D discrete systems available in the literature (Hanba, 2020; Hua et al, 2018; Khald et al, 2019; Peng and Xu, 2019; Yang et al, 2020; Zhao et al, 2019). To name a few, Peng and Xu (2019) proposed a robust H ∞ filtering algorithm for 2D linear uncertain time-varying systems. Hanba (2020) gave a direct and converse Lyapunov theorem for an autonomous nonlinear 2D discrete system described by the Fornasini-Marchesini (FM) second model.…”

Finite-time boundedness of two-dimensional positive continuous-discrete systems in Roesser model

“…Over the past several decades, two-dimensional (2-D) systems have attracted great attention due to their applications in many areas, such as multidimensional digital filtering, linear image processing, signal processing, and process control (Du and Xie, 2002). The stability, control and filtering of 2-D discrete-time systems have been extremely investigated, and many important results are available in the literature (Bu et al, 2018; Chen et al, 2013; Dai and Guo, 2017; Hinamoto, 1997; Kurek, 2014; Lam et al, 2004; Peng and Xu, 2019; Peng et al, 2018; Tadepalli et al, 2015; Wu et al, 2007, 2008; Ye and Wang, 2011; Yeganefar, et al 2013). To name a few, stability criteria of 2-D discrete linear systems described as the Fornasini-Marchesini second model and the Roesser model were proposed in Hinamoto (1997) and Lam et al (2004).…”

“…To name a few, stability criteria of 2-D discrete linear systems described as the Fornasini-Marchesini second model and the Roesser model were proposed in Hinamoto (1997) and Lam et al (2004). Several stability conditions of 2-D discrete systems with time delays were presented in the literature (Bu et al, 2018; Chen et al, 2013; Dai and Guo, 2017; Kurek, 2014; Lam et al, 2004; Peng et al, 2018; Peng and Xu, 2019; Tadepalli et al, 2015; Wu et al, 2007, 2008; Ye and Wang, 2011; Yeganefar et al, 2013). H ∞ control or filtering of 2-D discrete systems were considered in Wu et al (2007, 2008).…”