On the time-varying Halanay inequality with applications to stability analysis of time-delay systems

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. (C) 2021 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

The paper presents improvements to the stability analysis of Halanay inequalities with time-varying coefficients, establishing three classes of improved conditions to ensure uniformly exponentially stable solutions. The new conditions allow for unbounded and sign-indefinite coefficients, achieved through the use of uniformly asymptotic stable functions. Based on these improved stability conditions, sufficient criteria are developed for testing the stability of time-varying time-delay systems. The advantages of the proposed methods are illustrated through numerical examples borrowed from literature.