This paper focuses on the stability analysis of nonlinear time-delay systems on time scales, which are of generality as they can include not only the traditional continuous and discrete ones, but also some other cases, such as systems on general uniform or non-uniform time domains. One existing classical method for analyzing stability of such systems is the Razumikhin-type theorem with requiring the time derivative of relating Lyapunov function to be non-positive for uniform stability and negative for uniform asymptotic or exponential stability, which are difficult to be satisfied. To relax these restrictions, by introducing the time-scale type uniformly stable function and uniformly asymptotically stable function, this paper presents several less conservative stability criteria, in which the time-scale time derivative of Lyapunov function can be positive or non-negative. To demonstrate the effectiveness of the theoretic results, a numerical example about non-continuous and non-discrete time-delay systems is given.

本文重点研究时间尺度上非线性时滞系统的稳定性分析，它具有一般性，不仅可以包括传统的连续和离散系统，还可以包括其他一些情况，例如一般均匀或非均匀系统上的系统。时域。现有的一种分析此类系统稳定性的经典方法是Razumikhin型定理，该定理要求相关Lyapunov函数的时间导数对于均匀稳定性为非正值，对于均匀渐近或指数稳定性为负值，难以满足。为了放宽这些限制，本文通过引入时间尺度型一致稳定函数和一致渐近稳定函数，提出了几个不太保守的稳定性准则，其中李雅普诺夫函数的时间尺度时间导数可以是正的也可以是非负的。为了证明理论结果的有效性，给出了一个非连续非离散时滞系统的数值例子。