The main results of the paper are improvements on the stability analysis of Halanay inequalities with time-varying coefficients in both continuous-time and discrete-time setting. Three classes of improved conditions are established to ensure that the solution to the Halanay inequality is uniformly exponentially stable. The merit of the proposed new conditions is that the coefficients of the Halanay inequality can be unbounded and sign indefinite. This is achieved by using the notion and properties of uniformly asymptotic stable (UAS) functions. Based on the improved stability conditions for the Halanay inequality and the Lyapunov Razumikhin approach, three classes of sufficient conditions are established for testing the stability of time-varying time-delay systems. Finally, the advantages of the proposed methods are illustrated by some numerical examples with some of them borrowed from the literature.

本文的主要结果是改进了连续时间和离散时间设置下具有时变系数的 Halanay 不等式的稳定性分析。建立三类改进条件以确保 Halanay 不等式的解是一致指数稳定的。提议的新条件的优点是 Halanay 不等式的系数可以是无界的并且符号不定。这是通过使用均匀渐近稳定 (UAS) 函数的概念和性质来实现的。基于改进的 Halanay 不等式稳定性条件和 Lyapunov Razumikhin 方法，建立了三类充分条件来检验时变时滞系统的稳定性。最后，