Qualitative Analyses of Differential Systems with Time-Varying Delays via Lyapunov-Krasovskii Approach

Tunç C., Tunç O., Wang Y., Yao J.

MATHEMATICS, vol.9, no.11, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 11
  • Publication Date: 2021
  • Doi Number: 10.3390/math9111196
  • Journal Name: MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: system of non-linear DDEs, uniformly asymptotically stability, integrability, boundedness at infinity, Lyapunov-Krasovskii approach, time-varying delay, STABILITY, BOUNDEDNESS, EQUATIONS
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this paper, a class of systems of linear and non-linear delay differential equations (DDEs) of first order with time-varying delay is considered. We obtain new sufficient conditions for uniform asymptotic stability of zero solution, integrability of solutions of an unperturbed system and boundedness of solutions of a perturbed system. We construct two appropriate Lyapunov-Krasovskii functionals (LKFs) as the main tools in proofs. The technique of the proofs depends upon the Lyapunov-Krasovskii method. For illustration, two examples are provided in particular cases. An advantage of the new LKFs used here is that they allow to eliminate using Gronwall's inequality. When we compare our results with recent results in the literature, the established conditions are more general, less restrictive and optimal for applications.