Global exponential synchronization of delayed BAM neural networks with reaction-diffusion terms and the Neumann boundary conditions

Zhang, Weiyuan; Li, Junmin

doi:10.1186/1687-2770-2012-2

Cited by 12 publications

(17 citation statements)

References 28 publications

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“…In proof of Theorem 1, the new Lyapunov-Krasovskii functional to be constructed is more general. The adaptive synchronization criteria in the literature [22][23][24] are independent on the measure of the space and diffusion effects. However, in this paper, the obtained results are dependent on the measure of the space and diffusion effects.…”

Section: Proof Consider Lyapunov-krasovskii Functional Asmentioning

confidence: 99%

Adaptive stochastic synchronization of delayed reaction–diffusion neural networks

Zhang

Sun

et al. 2020

Measurement and Control

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In this paper, we deal with the adaptive stochastic synchronization for a class of delayed reaction–diffusion neural networks. By combing Lyapunov–Krasovskii functional, drive-response concept, the adaptive feedback control scheme, and linear matrix inequality method, we derive some sufficient conditions in terms of linear matrix inequalities ensuring the stochastic synchronization of the addressed neural networks. The output coupling with delay feedback and the update laws of parameters for adaptive feedback control are proposed, which will be of significance in the real application. The novel Lyapunov–Krasovskii functional to be constructed is more general. The derived results depend on the measure of the space, diffusion effects, and the upper bound of derivative of time-delay. Finally, an illustrated example is presented to show the effectiveness and feasibility of the proposed scheme.

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Section: Proof Consider Lyapunov-krasovskii Functional Asmentioning

confidence: 99%

Adaptive stochastic synchronization of delayed reaction–diffusion neural networks

Zhang

Sun

et al. 2020

Measurement and Control

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“…Obviously, the error dynamics in (14) is nonlinear. For the stability of nonlinear dynamical systems, various results have been derived in [21][22][23][24][25][26][27]. For convenience, the stability of (14) can be analyzed by using Lyapunov indirect method.…”

Section: Stability Of Open-loop Operationmentioning

confidence: 99%

On Stability of Open-Loop Operation without Rotor Information for Brushless DC Motors

Lyu

Shi³

et al. 2014

Mathematical Problems in Engineering

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Open-loop operation mode is often used to control the Brushless DC Motors (BLDCMs) without rotor position sensors when the back electromotive force (EMF) is too weak due to the very low rotor velocity. The rotor position information is not necessary in this mode and the stator windings are supplied with voltages under a certain ratio of the amplitude to the frequency. However, the rotor synchronization will be destroyed once if the commutation instant is inappropriate. In order to improve the reliability of the open-loop operation mode, a dynamic equation is established to represent the synchronization error between the rotor and the stator. Thereafter, the stability of the open-loop control mode is analyzed by using Lyapunov indirect method. Theoretical analysis indicates that the open-loop control mode is asymptotically stable only when the commutation instant of the stator current lags behind the ideal one suitably. Finally, theoretical analysis is verified through the experimental results of a certain BLDCM.

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“…Generally, an important precondition of the applications mentioned above is that the equilibrium of the BAM neural networks should be stable to some extent. So the stability analysis for neural networks has been attracting wide publicity ( [2][3][4][5][6] and their references therein).…”

Section: Introductionmentioning

confidence: 99%

“…In addition, diffusion effect exists really in the neural networks when electrons are moving in asymmetric electromagnetic fields. Thereby, reaction-diffusion factor should be considered in any neural networks model [2,[4][5][6][7][15][16][17]. Besides, time-delays also occur unavoidably owing to the finite switching speed of neurons and amplifiers.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

LMI-Based Stability Criterion for Impulsive Delays Markovian Jumping Time-Delays Reaction-Diffusion BAM Neural Networks via Gronwall-Bellman-Type Impulsive Integral Inequality

Rao

Wang

Zhong

2015

Mathematical Problems in Engineering

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Lyapunov stability theory, variational methods, Gronwall-Bellman-type inequalities theorem, and linear matrices inequality (LMI) technique are synthetically employed to obtain the LMI-based global stochastic exponential stability criterion for a class of time-delays Laplace diffusion stochastic equations with large impulsive range under Dirichlet boundary value, whose backgrounds of physics and engineering are the impulsive Markovian jumping time-delays reaction-diffusion BAM neural networks. As far as the authors know, it is the first time to derive the LMI-based criterion by way of Gronwall-Bellman-type inequalities, which can be easily and efficiently computed by computer Matlab LMI toolbox. And the obtained criterion improves the allowable upper bounds of impulse against those of some previous related literature. Moreover, a numerical example is presented to illustrate the effectiveness of the proposed methods.

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Global exponential synchronization of delayed BAM neural networks with reaction-diffusion terms and the Neumann boundary conditions

Cited by 12 publications

References 28 publications

Adaptive stochastic synchronization of delayed reaction–diffusion neural networks

Adaptive stochastic synchronization of delayed reaction–diffusion neural networks

On Stability of Open-Loop Operation without Rotor Information for Brushless DC Motors

LMI-Based Stability Criterion for Impulsive Delays Markovian Jumping Time-Delays Reaction-Diffusion BAM Neural Networks via Gronwall-Bellman-Type Impulsive Integral Inequality

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