A New Delay-Dependent Stability Criterion for Uncertain 2-D Discrete Systems Described by Roesser Model Under the Influence of Quantization/Overflow Nonlinearities

On reachable set estimation of two‐dimensional systems described by the Roesser model with time‐varying delays

“…Note also that and . Thus, when α approaches 1, the inequalities in Equations and are reduced to 2‐D Jensen‐type inequalities given in Chen and Tadepalli et al…”

“…While the problem of stability analysis and controller design has been well developed for one‐dimensional (1‐D) systems with delays, such theory for 2‐D systems has just received growing research attention recently. For example, in previous studies, the problem of stability was studied for 2‐D discrete‐time systems with time‐varying delays coupled with saturation and quantization nonlinearities. By introducing slack matrix variables and using sector based characterisation of the nonlinearities, delay‐dependent stability conditions were derived in terms of linear matrix inequalities (LMIs).…”

Stability analysis of two-dimensional Markovian jump state-delayed systems in the Roesser model with uncertain transition probabilities

“…While stability analysis and control of onedimensional (1-D) delayed systems has been widely studied and developed, this problem for 2-D systems has gained growing attention recently. Particularly, in [5,29], delay-dependent stability conditions were proposed for discretetime 2-D systems with time-varying delays in the presence of saturation and quantization nonlinearities. By utilizing the free-weighting matrix technique, delay-dependent robust stability conditions were derived in [40] for a class of 2-D systems described by the second FM model with delays and uncertainties.…”

Global exponential stability of 2D switched positive nonlinear systems described by the Roesser model

“…Two‐dimensional (2D) systems, in which the information propagation occurs in each of the two independent directions, appear in many practical applications, such as image processing, multidimensional digital filtering, and circuit analysis (see, eg, other works and the references therein). Due to their structures and applications, the Roesser model and the Fornasini‐Marchesini model are the most frequently used to describe 2D systems and have attracted considerable attention in the past few decades . In particular, some results on the dynamical properties of 2D positive systems have been reported .…”

“…Due to their structures and applications, the Roesser model and the Fornasini-Marchesini model are the most frequently used to describe 2D systems 1,4,5 and have attracted considerable attention in the past few decades. [6][7][8] In particular, some results on the dynamical properties of 2D positive systems have been reported. [9][10][11] Positive dynamical systems are those systems, whose state variables are nonnegative whenever the initial conditions are nonnegative.…”