We study the stability of general n-dimensional nonautonomous linear differential equations with infinite delays. Delay independent criteria, as well as criteria depending on the size of some finite delays are established. In the first situation, the effect of the delays is dominated by non-delayed diagonal negative feedback terms, and sufficient conditions for both the asymptotic and the exponential asymptotic stability of the system are given. In the second case, the stability depends on the size of some bounded diagonal delays and coefficients, although terms with unbounded delay may co-exist. Our results encompass DDEs with discrete and distributed delays, and enhance some recent achievements in the literature.

我们研究了具有无限时滞的一般n维非自治线性微分方程的稳定性。建立了独立于延迟的准则，以及取决于某些有限延迟的大小的准则。在第一种情况下，延迟的影响受非延迟对角负反馈项的支配，并且给出了系统渐近和指数渐近稳定性的充分条件。在第二种情况下，稳定性可能取决于一些有界对角线延迟和系数的大小，尽管具有无界延迟的项可能会共存。我们的结果包括具有离散和分布式延迟的DDE，并增强了文献中的一些最新成果。