One-dimensional (1-D) monotone systems have received considerable attention recently due to their wide applicability and interesting mathematical properties. One of these special properties is that, for LTI monotone systems, exponential stability is insensitive to time-delays. Some extensions to 1-D nonlinear monotone systems based on conditions of homogeneity have also been reported. In this paper, we study the problem of exponential stability of discrete-time 2-D nonlinear monotone systems described by the Roesser model with time-varying delays. Specifically, based on the monotone property and homogeneity of the associated vector fields, necessary and sufficient delay-independent exponential stability conditions are derived. The magnitudes of delays are also taken into deriving an explicit estimation of the exponential decay rate which correlates the impact of delays on the system performance. Two examples are given to demonstrate the effectiveness of the obtained results.

中文翻译：

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有界方向时滞二维齐次单调系统的指数稳定性


一维（1-D）单调系统由于其广泛的适用性和有趣的数学特性最近受到了相当大的关注。这些特殊属性之一是，对于 LTI 单调系统，指数稳定性对时滞不敏感。还报道了基于均匀性条件的一维非线性单调系统的一些扩展。在本文中，我们研究了时变时滞Roesser模型描述的离散时间二维非线性单调系统的指数稳定性问题。具体而言，基于相关矢量场的单调性和同质性，推导了必要且充分的时滞无关指数稳定性条件。延迟的大小也被考虑到得出指数衰减率的明确估计，该指数衰减率与延迟对系统性能的影响相关。给出了两个例子来证明所得结果的有效性。