Qualitative Analyses of Differential Systems with Time-Varying Delays via Lyapunov–Krasovski? Approach

Cemil Tunç, Osman Tunç, Yuanheng Wang and Jen-Chih Yao
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Cemil Tunç: Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Campus, Van 65080, Turkey
Osman Tunç: Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Campus, Van 65080, Turkey
Yuanheng Wang: Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
Jen-Chih Yao: Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 404332, Taiwan

Mathematics, 2021, vol. 9, issue 11, 1-20

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–Krasovski? functionals (LKFs) as the main tools in proofs. The technique of the proofs depends upon the Lyapunov–Krasovski? 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.

Keywords: system of non-linear DDEs; uniformly asymptotically stability; integrability; boundedness at infinity; Lyapunov–Krasovski? approach; time-varying delay (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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