scholarly journals Further remarks on Markus-Yamabe instability for time-varying delay differential equations∗∗This work was partially supported by the DIGITEO grant SSy-CoDyC and by the Laboratoire des Signaux et Systemes (L2S), and in the framework of the iCODE institute, research project of the Idex Paris-Saclay.

2015 ◽  
Vol 48 (12) ◽  
pp. 33-38 ◽  
Author(s):  
I. Haidar ◽  
P. Mason ◽  
S.I. Niculescu ◽  
M. Sigalotti ◽  
A. Chaillet
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Time Varying ◽  
Research Project ◽  
Time Varying Delay ◽  
Delay Differential ◽  
Varying Delay

scholarly journals The Semimartingale Approach to Almost Sure Stability Analysis of a Two-Stage Numerical Method for Stochastic Delay Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qian Guo ◽  
Xueyin Tao
Keyword(s):  
Differential Equation ◽  
Numerical Experiments ◽  
Time Varying ◽  
Almost Sure Stability ◽  
Stochastic Delay ◽  
Almost Sure Exponential Stability ◽  
Time Varying Delay ◽  
Backward Euler ◽  
Delay Differential ◽  
Varying Delay

Almost sure exponential stability of the split-step backward Euler (SSBE) method applied to an Itô-type stochastic differential equation with time-varying delay is discussed by the techniques based on Doob-Mayer decomposition and semimartingale convergence theorem. Numerical experiments confirm the theoretical analysis.

scholarly journals Qualitative Analyses of Differential Systems with Time-Varying Delays via Lyapunov–Krasovskiĭ Approach

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1196
Author(s):  
Cemil Tunç ◽  
Osman Tunç ◽  
Yuanheng Wang ◽  
Jen-Chih Yao
Keyword(s):  
Sufficient Conditions ◽  
Zero Solution ◽  
Unperturbed System ◽  
Time Varying ◽  
Time Varying Delay ◽  
Gronwall’S Inequality ◽  
Perturbed System ◽  
Linear Delay ◽  
Delay Differential ◽  
Varying Delay

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

New finite-time stability analysis of singular fractional differential equations with time-varying delay

2020 ◽  
Vol 23 (2) ◽  
pp. 504-519 ◽  
Author(s):  
Nguyen T. Thanh ◽  
Vu N. Phat ◽  
Piyapong Niamsup
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Finite Time ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Singular Fractional Differential Equations ◽  
Fractional Differential ◽  
Varying Delay

AbstractThe Lyapunov function method is a powerful tool to stability analysis of functional differential equations. However, this method is not effectively applied for fractional differential equations with delay, since the constructing Lyapunov-Krasovskii function and calculating its fractional derivative are still difficult. In this paper, to overcome this difficulty we propose an analytical approach, which is based on the Laplace transform and “inf-sup” method, to study finite-time stability of singular fractional differential equations with interval time-varying delay. Based on the proposed approach, new delay-dependent sufficient conditions such that the system is regular, impulse-free and finite-time stable are developed in terms of a tractable linear matrix inequality and the Mittag-Leffler function. A numerical example is given to illustrate the application of the proposed stability conditions.

Existence and Hyers-Ulam stability results for a class of fractional order delay differential equations with non-instantaneous impulses

2020 ◽  
Vol 70 (5) ◽  
pp. 1231-1248
Author(s):  
Danfeng Luo ◽  
Zhiguo Luo
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Existence Results ◽  
Time Varying ◽  
Ulam Stability ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Gronwall’S Inequality ◽  
Fractional Differential ◽  
Delay Differential ◽  
Stability Results

AbstractIn this paper, we mainly consider the existence and Hyers-Ulam stability of solutions for a class of fractional differential equations involving time-varying delays and non-instantaneous impulses. By the Krasnoselskii’s fixed point theorem, we present the new constructive existence results for the addressed equation. In addition, we deduce that the equations have Hyers-Ulam stable solutions by utilizing generalized Grönwall’s inequality. Some results in this literature are new and improve some early conclusions.

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