The problem of delay-dependent stability is concerned for two-dimensional discrete-time systems with interval time-varying delays in this paper. Choosing a Lyapunov functional with the upper bound and lower bound of delays, considering all terms in the difference and using two-dimensional Abel lemma-based finite-sum inequalities, a new delay-dependent stability criterion in terms of linear matrix inequality is derived for two-dimensional discrete-time systems. Then, based on the delay-dependent stability criteria, a state feedback control problem and a dynamic output feedback control problem are considered to realize the stability control for the two-dimensional discrete-time system. Finally, it is shown through four numerical examples that the stability criterion can provide a larger admissible maximum upper bound with less decision variables than the stability criterion using two-dimensional Jensen inequalities approach.

中文翻译：

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基于 Abel 引理的有限和不等式稳定二维时变延迟系统

本文研究了具有区间时变时滞的二维离散时间系统的时滞相关稳定性问题。选择具有时滞上下界的李雅普诺夫泛函，考虑差分中的所有项，并利用基于二维阿贝尔引理的有限和不等式，推导出线性矩阵不等式方面的时滞相关稳定性新判据二维离散时间系统。然后，基于时滞相关的稳定性判据，考虑状态反馈控制问题和动态输出反馈控制问题，实现二维离散时间系统的稳定性控制。最后，