Overflow oscillations‐free realization of discrete‐time 2D Roesser models under quantization and overflow constraints

Abstract

This brief proposes novel linear matrix inequalities-based criteria to investigate the asymptotic convergence of states to an overflow oscillations-free ellipsoidal region for a two-dimensional Roesser digital model subjected to quantization and overflow effects of a digital hardware. Existence of a novel region for two-dimensional Rosser systems is shown in the present study, in which overflow oscillations can be completely removed for realization of a system. New realization conditions for Roesser systems in the absence and presence of external interference along with stability and overflow-free regional behavior are investigated by application of regional analysis, convex routines, and Lyapunov redesign. In contrast to existing literature that primarily focus on a specific type of quantitation and global asymptotic stability, the conditions in the presented work are derived by considering the generalized quantization arithmetic and for guaranteeing convergence of states in a convex oscillations-free region (in the steady-state) in both the absence and presence of bounded interference. The localized stable regions can be directly associated with the word-length employed to realize the two-dimensional systems on a digital hardware. Simulation results are also furnished to validate the efficacy of the proposed approach.

Stability of uncertain 2-D discrete delayed systems with saturation

“…As a result, investigating the GAS of 2-D DSs employing time-varying delays (TVDs) is an important research topic. Several authors have paid attention to the problem of GAS in 2-D delayed DSs [15][16][17][19][20][21].…”

“…It is worth noting that Equations 1-5 cover a broad range of 2-D practical uncertain systems with TVDs and SNL. Such systems cover 2-D control systems [32] with SNL [16], 2-D DSs employed on a digital signal processor [33], wireless sensor networks [34], vehicle control systems [35], networked control systems [36], etc.…”

“…It may frequently occur in realistic systems owing to transmission delays, measurement delays, computational delays, etc. The presence of delay in practical systems may cause undesired transient responses and, thus, lead the system towards instability [9,[13][14][15][16][17][18][19][20][21][22].…”

H∞ filtering for continuous fractional‐order 2D Roesser model: The 0<α≤1 case

“…Nowadays, an increased number of scholars have a strong interest in the research of two-dimensional (2D) systems [1][2][3][4]. Different from one-dimensional (1D) systems, the state space of 2D systems has two dimensions, which can describe more system information.…”

Robust ∞ model reduction for the continuous fractional‐order two‐dimensional Roesser system: The 0 < ε ≤ 1 case

“…Over the past decades, an increasing number of scholars have participated in the study of 2D systems [1][2][3][4]. Two-dimensional (2D) systems differ from one-dimensional (1D) systems in that their state spaces have two dimensions; thus, 2D systems may typically describe more system information than 1D systems.…”