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

Natalya O. Sedova () and Olga V. Druzhinina
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Natalya O. Sedova: Department of Mathematics, Information and Aviation Technology, Ulyanovsk State University, 432017 Ulyanovsk, Russia
Olga V. Druzhinina: Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, 119333 Moscow, Russia

Mathematics, 2023, vol. 11, issue 4, 1-15

Abstract: 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.

Keywords: time-varying system; delay differential system; Razumikhin condition; exponential stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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