New generalized Halanay inequalities with applications to stability of nonlinear non-autonomous time-delay systems

Hien, Le Van; Phát, Vũ Ngọc; Trinh, Hieu

doi:10.1007/s11071-015-2176-0

Cited by 61 publications

(43 citation statements)

References 31 publications

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“…Since M 1 = −D +ÂF is a Metzler matrix and M 2 = B + G ≥ 0, (11) is a positive system [34]. Furthermore, by some similar lines used in the proof of Lemma 2.1 in [14], it is found…”

Section: Theorem 1 Let Assumptions (A1)-(a4) Hold Then the Impulsivementioning

confidence: 83%

See 1 more Smart Citation

Exponential Stability of Non-Autonomous Neural Networks with Heterogeneous Time-Varying Delays and Destabilizing Impulses

Hien

Loan

2016

Vietnam J. Math.

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In this paper, the problem of global exponential stability analysis of a class of non-autonomous neural networks with heterogeneous delays and time-varying impulses is considered. Based on the comparison principle, explicit conditions are derived in terms of testable matrix inequalities ensuring that the system is globally exponentially stable under destabilizing impulsive effects. Numerical examples are given to demonstrate the effectiveness of the obtained results.

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“…Since M 1 = −D +ÂF is a Metzler matrix and M 2 = B + G ≥ 0, (11) is a positive system [34]. Furthermore, by some similar lines used in the proof of Lemma 2.1 in [14], it is found…”

Section: Theorem 1 Let Assumptions (A1)-(a4) Hold Then the Impulsivementioning

confidence: 83%

“…Inspired by the technique used in the proof of generalized Halanay inequalities [14,36], we now show thatẑ…”

Section: Theorem 1 Let Assumptions (A1)-(a4) Hold Then the Impulsivementioning

confidence: 96%

Exponential Stability of Non-Autonomous Neural Networks with Heterogeneous Time-Varying Delays and Destabilizing Impulses

Hien

Loan

2016

Vietnam J. Math.

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“…Recent results on global asymptotic stability for delay differential systems can be found in [9,10,17,22].…”

Section: Discussionmentioning

confidence: 99%

New exponential stability conditions for linear delayed systems of differential equations

Berezansky¹,

Diblı́k²,

Svoboda³

et al. 2016

Proceedings of the 10'th Colloquium on the Qualitative Theory of Differential Equations (July 1–4, 2015, Szeged, Hungary) Edite

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Abstract. New explicit results on exponential stability, improving recently published results by the authors, are derived for linear delayed systemṡwhere t ≥ 0, m and r ij , i, j = 1, . . . , m are natural numbers, a k ij : [0, ∞) → R are measurable coefficients, and h k ij : [0, ∞) → R are measurable delays. The progress was achieved by using a new technique making it possible to replace the constant 1 by the constant 1 + 1/e on the right-hand sides of crucial inequalities ensuring exponential stability.

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“…On the other hand, as mentioned in other works, it is a very interesting problem to find estimate of the convergent rate of solution for nonlinear systems. However, in some special cases, the convergence rate of the synchronization cannot be shown or it is not easy to estimate . For example, consider the differential equation

\overset{y}{true} false(x false) = - \frac{1}{2} y^{3}

, x ≥ 0.…”

Section: Introductionmentioning

confidence: 97%

“…Therefore, realizing synchronization between master‐salve chaotic systems via introducing an output feedback controller is more desirable and indeed very important in both theory and applications, which is yet a quite challenging problem . On the other hand, as mentioned in other works, it is a very interesting problem to find estimate of the convergent rate of solution for nonlinear systems. However, in some special cases, the convergence rate of the synchronization cannot be shown or it is not easy to estimate .…”

Section: Introductionmentioning

confidence: 99%

Nonlinear output control scheme for general decay synchronization of delayed neural networks with inertial term

Abdurahman

Jiang

Sader

2019

Intl J Robust & Nonlinear

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Summary This study is mainly concerned with the general decay synchronization (GDS) problem of a class of inertial neural networks (INNs) with time‐varying delay. First, unlike the methods used in previous relevant literature where both of the master and slave systems were transferred into the first‐order differential equations, only error dynamical system is transferred into the reduced‐order differential equation. Then, by designing a novel nonlinear output feedback controller and constructing suitable Lyapunov functionals, some simple and useful sufficient conditions ensuring the GDS of considered INNs are established via employing useful analysis techniques and linear matrix inequality approach. In addition, two examples are presented to show the effectiveness of the established theoretical results.

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New generalized Halanay inequalities with applications to stability of nonlinear non-autonomous time-delay systems

Cited by 61 publications

References 31 publications

Exponential Stability of Non-Autonomous Neural Networks with Heterogeneous Time-Varying Delays and Destabilizing Impulses

Exponential Stability of Non-Autonomous Neural Networks with Heterogeneous Time-Varying Delays and Destabilizing Impulses

New exponential stability conditions for linear delayed systems of differential equations

Nonlinear output control scheme for general decay synchronization of delayed neural networks with inertial term

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