Exponential Stability of Nonlinear Time-Varying Delay Differential Equations via Lyapunov-Razumikhin Technique

被引：1

作者：

Sedova, Natalya O. ^{[1
]}

Druzhinina, Olga V. ^{[2
,3
]}

机构：

[1] Ulyanovsk State Univ, Dept Math Informat & Aviat Technol, Ulyanovsk 432017, Russia

[2] Russian Acad Sci, Fed Res Ctr Comp Sci & Control, Moscow 119333, Russia

[3] Russian Acad Sci, VA Trapeznikov Inst Control Sci, Moscow 117997, Russia

来源：

MATHEMATICS | 2023年 / 11卷 / 04期

关键词：

time-varying system; delay differential system; Razumikhin condition; exponential stability; UNIFORM ASYMPTOTIC STABILITY; STATE STABILITY; SYSTEMS; CRITERIA; THEOREM; INPUT; DECAY;

D O I：

10.3390/math11040896

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, some new sufficient conditions for the exponential stability of nonlinear time-varying delay differential equations are given. An extension of the classical asymptotical stability theorem in terms of a Lyapunov-Razumikhin function is obtained. The condition of non-positivity of the time derivative of a Razumikhin function is weakened. Additionally, the resulting sufficient asymptotic stability conditions allow us to guarantee uniform exponential stability and evaluate the exponential convergence rate of the system solutions. The effectiveness of the results is demonstrated by some examples.

引用

页数：15

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