Mean square exponential stability of stochastic delayed Hopfield neural networks

Wan, Li; Sun, Jian

doi:10.1016/j.physleta.2005.06.024

Cited by 186 publications

(77 citation statements)

References 23 publications

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“…Therefore, it is of practical importance to study the stochastic effects on the stability property of delayed neural networks, see for example [3][4][5][6]11,16,18,19,23,27,29]. Also, there are systems which are with some nonzero delays, but they are unstable without delay [7,8,30].…”

Section: Introductionmentioning

confidence: 99%

Delay-dependent exponential stability results for uncertain stochastic Hopfield neural networks with interval time-varying delays

2012

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This paper is concerned with stability analysis problem for uncertain stochastic neural networks with interval time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Both the cases of the time-varying delays which may be differentiable and may not be differentiable are considered in this paper. Based on the Lyapunov-Krasovskii functional and stochastic stability theory, delay/interval-dependent stability criteria are obtained in terms of linear matrix inequalities. Some stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), by introducing some free-weighting matrices. Finally, three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions. Mathematics Subject Classification (2010) 34K20 · 34K50 · 92B20

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Section: Introductionmentioning

confidence: 99%

Delay-dependent exponential stability results for uncertain stochastic Hopfield neural networks with interval time-varying delays

2012

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“…Recently, Wan and Sun [19] studied the mean square exponential stability of stochastically perturbed Hopfield-type neural networks with constant fixed time delays (1) …”

Section: Introductionmentioning

confidence: 99%

“…In this paper, motivated by [12], [17], [19], we consider the problem of mean square exponential stability for a class of uncertain stochastic Hopfield neural networks with discrete delays. By using the Lyapunov functional technique and stochastic analysis, an unified LMI approach is developed to establish sufficient conditions for the neural networks to be robustly, exponentially stable in the mean square.…”

Section: Introductionmentioning

confidence: 99%

New Result Concerning Mean Square Exponential Stability of Uncertain Stochastic Delayed Hopfield Neural Networks

Bai¹

2011

Bulletin of the Korean Mathematical Society

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Abstract. By using the Lyapunov functional method, stochastic analysis, and LMI (linear matrix inequality) approach, the mean square exponential stability of an equilibrium solution of uncertain stochastic Hopfield neural networks with delayed is presented. The proposed result generalizes and improves previous work. An illustrative example is also given to demonstrate the effectiveness of the proposed result.

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“…Results in 5,6 suggested that the neural networks can be stabilized or destabilized by certain stochastic inputs, which implies that it is important to consider the noise effects in the stability analysis for the neural networks. Recently, the study of stochastic neural networks has drawn much attentions from researchers all over the world and some results can be found in 7,8,9,10,11,12,13,22 and the references cited therein 15,16,17,19,21 . But for the study of stochastic CGNN, up till now, there are only a few results 10,11,14,20 .…”

Section: Introductionmentioning

confidence: 99%

Exponential stability analysis for delayed stochastic Cohen-Grossberg neural network

Wang¹,

Liang²

2010

IJCIS

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In this paper, the exponential stability problems are addressed for a class of delayed Cohen-Grossberg neural networks which are also perturbed by some stochastic noises. By employing the Lyapunov method, stochastic analysis and some inequality techniques, sufficient conditions are acquired for checking the pth(p > 1) and the 1st moment exponential stability of the network. Finally, One example is given to show the effectiveness of the proposed results.

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Mean square exponential stability of stochastic delayed Hopfield neural networks

Cited by 186 publications

References 23 publications

Delay-dependent exponential stability results for uncertain stochastic Hopfield neural networks with interval time-varying delays

Delay-dependent exponential stability results for uncertain stochastic Hopfield neural networks with interval time-varying delays

New Result Concerning Mean Square Exponential Stability of Uncertain Stochastic Delayed Hopfield Neural Networks

Exponential stability analysis for delayed stochastic Cohen-Grossberg neural network

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