Delay-dependent exponential stability of cellular neural networks with time-varying delays

ZHANG, Q; Wei, Xingchen; Xu, Jianqiang

doi:10.1016/s0960-0779(04)00391-1

Cited by 91 publications

(47 citation statements)

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“…Remark 5.1. The particular model (5.3) was recently studied in several papers such as [21], [22], and [11]. By comparison, for example, we can apply Corollary 5.1 to conclude that the particular model…”

Section: Applicationsmentioning

confidence: 86%

Global exponential stability of nonautonomous neural network models with continuous distributed delays

Esteves¹,

Gökmen²,

Oliveira³

2013

Applied Mathematics and Computation

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For a family of non-autonomous differential equations with distributed delays, we give sufficient conditions for the global exponential stability of an equilibrium point. This family includes most of the delayed models of neural networks of Hopfield type, with time-varying coefficients and distributed delays. For these models, we establish sufficient conditions for their global exponential stability. The existence and global exponential stability of a periodic solution is also addressed. A comparison of results shows that these results are general, news, and add something new to some earlier publications.

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Section: Applicationsmentioning

confidence: 86%

Global exponential stability of nonautonomous neural network models with continuous distributed delays

Esteves¹,

Gökmen²,

Oliveira³

2013

Applied Mathematics and Computation

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“…Lemma 3 (see Zhang et al [26]; Zheng et al [27]) Assuming that function g j (s) is defined such that 0 g j (s)/s j ( j >0), then the following inequality holds…”

Section: Lemma 1 (See Sanchez and Perezmentioning

confidence: 99%

Novel stability criteria of Cohen–Grossberg neural networks with time‐varying delays

Zheng¹,

Shan²,

Wang³

2010

Circuit Theory & Apps

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SUMMARYIn this paper, a class of Cohen-Grossberg neural networks with time-varying delays is investigated. Based on several new Lyapunov-Krasovskii functionals, by employing the homeomorphism mapping principle, the Halanay inequality, a nonlinear measure approach and linear matrix inequality techniques, several delay-independent sufficient criteria are obtained for the existence, uniqueness and globally exponential stability of considered neural networks. Without assuming the boundedness and monotonicity of activation functions, the obtained conditions generalize some previous results in the literature. Two examples are also given to show the less conservativeness of the obtained conditions.

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“…Since the system contains variable coefficients, the results in [2][3][4]18] also cannot be applied to this example.…”

Section: An Examplementioning

confidence: 99%

“…So, stability of DCNNs has attracted many reseachers' attention, see, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13] and the references cited therein. In [2][3][4] Zhang et al have discussed global exponential convergence analysis of delayed neural networks with time-varying delays. In [10], Liao et al have utilized LMI approach to study asymptotically stability analysis of delayed neural networks.…”

Section: Introductionmentioning

confidence: 99%

Global exponential stability analysis for cellular neural networks with variable coefficients and delays

Kao

Gao

2007

Neural Comput & Applic

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Some sufficient conditions for the global exponential stability of cellular neural networks with variable coefficients and time-varying delays are obtained by a method based on a delayed differential inequality. The method, which does not make use of Lyapunov functionals, is simple and effective for the stability analysis of cellular neural networks with variable coefficients and timevarying delays. Some previous results in the literature are shown to be special cases of our results.

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Delay-dependent exponential stability of cellular neural networks with time-varying delays

Cited by 91 publications

References 0 publications

Global exponential stability of nonautonomous neural network models with continuous distributed delays

Global exponential stability of nonautonomous neural network models with continuous distributed delays

Novel stability criteria of Cohen–Grossberg neural networks with time‐varying delays

Global exponential stability analysis for cellular neural networks with variable coefficients and delays

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