Addressed in this paper is the stability issue of discrete-time delayed coupled systems consisting of a difference equation and an algebraic equation in coupled states. First, a necessary and sufficient condition of exponential stability is proposed for coupled systems with constant delays. Second, periodicity and stability are investigated for periodic coupled systems. Third, based on the Lyapunov inequality, a necessary and sufficient condition is presented for exponential stability of general time-varying coupled systems. Finally, as an application of these results, stability of discrete-time singular systems is discussed.

中文翻译：

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时滞离散时间耦合系统的稳定性分析

本文讨论的是离散时间延迟耦合系统的稳定性问题，该系统由耦合状态下的差分方程和代数方程组成。首先，为具有恒定延迟的耦合系统提出了指数稳定性的充要条件。其次，研究了周期性耦合系统的周期性和稳定性。第三，基于李雅普诺夫不等式，给出了一般时变耦合系统指数稳定性的充要条件。最后，作为这些结果的应用，讨论了离散时间奇异系统的稳定性。