Browsing by Author "Wang, Yuanheng"

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Delay-Dependent Stability, Integrability and Boundedeness Criteria for Delay Differential Systems
(Mdpi, 2021) Tunc, Osman; Tunc, Cemil; Wang, Yuanheng
This paper deals with non-perturbed and perturbed systems of nonlinear differential systems of first order with multiple time-varying delays. Here, for the considered systems, easily verifiable and applicable uniformly asymptotic stability, integrability, and boundedness criteria are obtained via defining an appropriate Lyapunov-Krasovskii functional (LKF) and using the Lyapunov-Krasovskii method (LKM). Comparisons with a former result that can be found in the literature illustrate the novelty of the stability theorem and show new contributions to the qualitative theory of solutions. A discussion of two illustrative examples and the obtained results are presented.
New and Improved Criteria on Fundamental Properties of Solutions of Integro-Delay Differential Equations With Constant Delay
(Mdpi, 2021) Tunc, Cemil; Wang, Yuanheng; Tunc, Osman; Yao, Jen-Chih
This paper is concerned with certain non-linear unperturbed and perturbed systems of integro-delay differential equations (IDDEs). We investigate fundamental properties of solutions such as uniformly stability (US), uniformly asymptotically stability (UAS), integrability and instability of the un-perturbed system of the IDDEs as well as the boundedness of the perturbed system of IDDEs. In this paper, five new and improved fundamental qualitative results, which have less conservative conditions, are obtained on the mentioned fundamental properties of solutions. The technique used in the proofs depends on Lyapunov-Krasovski functionals (LKFs). In particular cases, three examples and their numerical simulations are provided as numerical applications of this paper. This paper provides new, extensive and improved contributions to the theory of IDDEs.
Qualitative Analyses of Differential Systems With Time-Varying Delays Via Lyapunov-Krasovskii Approach
(Mdpi, 2021) Tunc, Cemil; Tunc, Osman; Wang, Yuanheng; Yao, Jen-Chih
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.