In the existing papers considering the stability analysis of discrete-time systems with distributed delays via the Lyapunov-Krasovskii functional (LKF) method, the delay kernels are normally restricted to be non-negative. In this paper, we aim to remove such a restriction and deal with the stability analysis of systems with arbitrary delay kernels. For this purpose, a kernel-related summation inequality is first constructed. Then, a stability condition is derived based on the proposed inequality and a model transformation. Finally, two numerical examples are presented to show that the proposed stability condition not only has a wider scope of application and is less conservative than the existing ones.

中文翻译：

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基于核相关求和不等式及模型变换的任意时滞核离散时间系统稳定性分析


在现有的论文中，考虑通过 Lyapunov-Krasovskii 泛函（LKF）方法对具有分布式延迟的离散时间系统进行稳定性分析，延迟核通常限制为非负。在本文中，我们的目标是消除这种限制并处理具有任意延迟内核的系统的稳定性分析。为此，首先构建与核相关的求和不等式。然后，根据所提出的不等式和模型变换导出稳定性条件。最后，给出了两个数值例子，表明所提出的稳定性条件比现有的稳定性条件不仅具有更广泛的适用范围，而且保守性更小。