We study the delay–dependent stability of linear high-order delay differential systems of neutral type. We firstly derive a bound of the unstable eigenvalues of the neutral systems. The bound of the unstable eigenvalues involves only the norms of the matrices of lower size. Then, using the argument principle, we present some stability criterion that is a necessary and sufficient condition for the delay–dependent stability of the neutral systems. Furthermore, we provide an efficient numerical algorithm for checking the stability of the neutral systems. Some numerical examples are given to illustrate the main results which extend those in the literature.

中文翻译：

---

高阶中立型时滞微分方程系统的稳定性判据

我们研究中立型线性高阶时滞微分系统的时滞相关稳定性。我们首先导出中立系统的不稳定特征值的界。不稳定特征值的边界仅涉及较小尺寸矩阵的范数。然后，使用论证原理，我们提出了一些稳定性判据，这对于中立系统的时滞相关稳定性是必要的和充分的条件。此外，我们提供了一种有效的数值算法来检查中性系统的稳定性。给出了一些数值例子来说明主要结果，这些结果扩展了文献中的内容。