This paper is concerned with the construction of strict Lyapunov–Krasovskii functionals (LKFs) for analyzing the input-to-state stability (ISS) problem of nonlinear time-varying time-delay systems. With the help of a known non-strict LKF, a series of strict LKFs are constructed for both continuous and discrete time-varying time-delay systems. The proposed LKFs are linear functionals of the known non-strict LKF. Compared with previous results, the proposed strict LKFs are more general. Taking advantage of the concepts of uniformly exponentially stable (UES) and uniformly exponentially expanding (UEE), the assumption of boundedness on the scalar function is not required. The effectiveness of the proposed theoretical results is illustrated by a couple of numerical examples.

本文涉及用于分析非线性时变时滞系统的输入状态稳定性（ISS）问题的严格Lyapunov–Krasovskii泛函（LKF）的构造。借助已知的非严格LKF，可为连续和离散时变时滞系统构建一系列严格的LKF。提出的LKF是已知的非严格LKF的线性功能。与以前的结果相比，建议的严格LKF更为通用。利用均匀指数稳定（UES）和均匀指数展开（UEE）的概念，不需要假设标量函数的有界性。几个数值例子说明了所提出的理论结果的有效性。