Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks

Chen, Jiejie; Zeng, Zhigang; Jiang, Ping

doi:10.1016/j.neunet.2013.11.016

Cited by 502 publications

(171 citation statements)

References 40 publications

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“…Remark 1. Assumption 1 can be seen in many literatures [3,13,[15][16][17][18][19][22][23][24]. Besides, different from most of above works, in this paper, we assume that the Lipschitz constant L i is unknown.…”

Section: Assumptionmentioning

confidence: 99%

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Adaptive Synchronization for a Class of Uncertain Fractional-Order Neural Networks

Liu

Wang

et al. 2015

Entropy

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In this paper, synchronization for a class of uncertain fractional-order neural networks subject to external disturbances and disturbed system parameters is studied. Based on the fractional-order extension of the Lyapunov stability criterion, an adaptive synchronization controller is designed, and fractional-order adaptation law is proposed to update the controller parameter online. The proposed controller can guarantee that the synchronization errors between two uncertain fractional-order neural networks converge to zero asymptotically. By using some proposed lemmas, the quadratic Lyapunov functions are employed in the stability analysis. Finally, numerical simulations are presented to confirm the effectiveness of the proposed method.

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Section: Assumptionmentioning

confidence: 99%

“…By using the Mittag-Leffler function, M-matrix and linear feedback control, the synchronization problem for a class of fractional-order chaotic neural networks is studied in [3]. For more recent results concerning chaotic synchronization in fractional-order neural networks one can refer to [22][23][24] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Synchronization for a Class of Uncertain Fractional-Order Neural Networks

Liu

Wang

et al. 2015

Entropy

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“…They all read and approved the final version of the manuscript. 1 College of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, China. 2 Institute for Information and System Science, Xi'an Jiaotong University, Xi'an, 710049, China.…”

Section: Competing Interestsmentioning

confidence: 99%

Algebraical criteria of stability for delayed memristive neural networks

Wu¹,

Zeng²

2015

Adv Differ Equ

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Memristive neurodynamic systems find many potential applications in mixed analog-digital multichip neurogrid and integrated photo-supercapacitor nanotube arrays. Analysis and design of memristive neurodynamic systems have attracted a large amount of research interest. In this study, some new neurodynamic approaches are proposed for stability analysis of delayed memristive neural networks. Some less conservative stability criteria are established by considering the memristor multiport effect, which is ignored in the previous literature. Numerical examples are given to demonstrate the effectiveness of these stability criteria.

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“…Aghababa [44] designed a chatter-free terminal sliding mode controller for nonlinear fractional-order dynamical systems. The synchronization problems of FOHNNs have captured more and more researchers' attention [45][46][47][48]. Xi et al [22] have discussed SMC for uncertain FOHNNs.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Synchronization for Uncertain Delayed Fractional-Order Hopfield Neural Networks via Fractional-Order Sliding Mode Control

Meng

Wang

2018

Mathematical Problems in Engineering

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Adaptive synchronization for a class of uncertain delayed fractional-order Hopfield neural networks (FOHNNs) with external disturbances is addressed in this paper. For the unknown parameters and external disturbances of the delayed FOHNNs, some adaptive estimations are designed. Firstly, a fractional-order switched sliding surface is proposed for the delayed FOHNNs. Then, according to the fractional-order extension of the Lyapunov stability criterion, a fractional-order sliding mode controller is constructed to guarantee that the synchronization error of the two uncertain delayed FOHNNs converges to an arbitrary small region of the origin. Finally, a numerical example of two-dimensional uncertain delayed FOHNNs is given to verify the effectiveness of the proposed method.

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Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks

Cited by 502 publications

References 40 publications

Adaptive Synchronization for a Class of Uncertain Fractional-Order Neural Networks

Adaptive Synchronization for a Class of Uncertain Fractional-Order Neural Networks

Algebraical criteria of stability for delayed memristive neural networks

Adaptive Synchronization for Uncertain Delayed Fractional-Order Hopfield Neural Networks via Fractional-Order Sliding Mode Control

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