In the paper, Tian and Wang (Appl Math Lett 105:106325, 8 pp, 2020, Theorem 1) took into consideration a linear system of integro-delay differential equations (IDDEs) with constant time retardation. In Tian and Wang (2020), the authors proved a new and interesting theorem concerning asymptotically stability of zero solution of that linear system of IDDEs with constant time retardation. Tian and Wang (2020) constructed a new Lyapunov–Krasovskiĭ functional (LKF) and used that LKF to prove the related theorem on the asymptotically stability. To the best of the information, we would like to note that the asymptotically stability result of Tian and Wang (2020, Theorem 1) consists of very interesting and strong conditions. However, in this paper, we construct a more suitable LKF, then we obtain the result of Tian and Wang (2020, Theorem 1) for uniformly asymptotically stability of zero solution under very weaker condition using that LKF as well as we investigate the integrability of the norm and boundedness of solutions. For illustrative aims, in particular cases, two numerical examples are provided for the uniformly asymptotically stability of zero solution as well as integrability and boundedness of solutions. By this work, we do a contribution to the topic of the paper and relevant literature. The results of this paper have also new contributions to the former literature and they may useful for researchers working on the topics of this paper.

在本文中，Tian和Wang（Appl Math Lett 105：106325，8 pp，2020，定理1）考虑了具有恒定时滞的整数延迟微分方程（IDDE）的线性系统。在Tian和Wang（2020）中，作者证明了一个新的有趣定理，它关于具有恒定时间延迟的IDDEs线性系统的零解的渐近稳定性。Tian和Wang（2020）构造了一个新的Lyapunov–Krasovskiĭ泛函（LKF），并使用该LKF证明了渐近稳定性的相关定理。据我们所知，Tian and Wang（2020，Theorem 1）的渐近稳定结果包含非常有趣和强大的条件。但是，在本文中，我们构建了一个更合适的LKF，然后我们得到了Tian和Wang（2020，定理1）使用LKF在零条件下在非常弱的条件下的一致渐近稳定性，同时我们研究了范数的可积性和解的有界性。为了说明的目的，在特定情况下，提供了两个数值示例，用于零解的一致渐近稳定性以及解的可积性和有界性。通过这项工作，我们为论文的主题和相关文献做出了贡献。本文的结果对以前的文献也有新的贡献，对于研究本文主题的研究人员可能有用。为零解的一致渐近稳定性以及解的可积性和有界性提供了两个数值示例。通过这项工作，我们为论文的主题和相关文献做出了贡献。本文的结果对以前的文献也有新的贡献，对于研究本文主题的研究人员可能有用。为零解的一致渐近稳定性以及解的可积性和有界性提供了两个数值示例。通过这项工作，我们为论文的主题和相关文献做出了贡献。本文的结果对以前的文献也有新的贡献，对于研究本文主题的研究人员可能有用。