Exponential synchronization control of delayed memristive neural network based on canonical Bessel-Legendre inequality

Xingxing Song; Pengfei Zhi; Wanlu Zhu; Hui Wang; Haiyang Qiu; Xingxing Song; Pengfei Zhi; Wanlu Zhu; Hui Wang; Haiyang Qiu

doi:10.3934/math.2022262

AIMS Mathematics

2022, Volume 7, Issue 3: 4711-4734. doi: 10.3934/math.2022262

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Exponential synchronization control of delayed memristive neural network based on canonical Bessel-Legendre inequality

School of Electronic and Information Engineering, Jiangsu University of Science and Technology, Zhenjiang 212000, China

Received: 27 October 2021 Revised: 10 December 2021 Accepted: 20 December 2021 Published: 24 December 2021
MSC : 93C10, 93D05

In this paper, we study the exponential synchronization problem of a class of delayed memristive neural networks(MNNs). Firstly, a intermittent control scheme is designed to solve the parameter mismatch problem of MNNs. A discontinuous controller with two tunable scalars is designed, and the upper limit of control gain can be adjusted flexibly. Secondly, an augmented Lyaponov-Krasovskii functional(LKF) is proposed, and vector information of N-order canonical Bessel-Legendre(B-L) inequalities is introduced. LKF method is used to obtain the stability criterion to ensure exponential synchronization of the system. The conservatism of the result decreases with the increase of the order of the B-L inequality. Finally, the effectiveness of the main results is verified by two simulation examples.
- memristive neural network,
- exponential synchronization,
- canonical Bessel-Legendre inequality,
- discontinuous controller,
- LMI
Citation: Xingxing Song, Pengfei Zhi, Wanlu Zhu, Hui Wang, Haiyang Qiu. Exponential synchronization control of delayed memristive neural network based on canonical Bessel-Legendre inequality[J]. AIMS Mathematics, 2022, 7(3): 4711-4734. doi: 10.3934/math.2022262

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Abstract

In this paper, we study the exponential synchronization problem of a class of delayed memristive neural networks(MNNs). Firstly, a intermittent control scheme is designed to solve the parameter mismatch problem of MNNs. A discontinuous controller with two tunable scalars is designed, and the upper limit of control gain can be adjusted flexibly. Secondly, an augmented Lyaponov-Krasovskii functional(LKF) is proposed, and vector information of N-order canonical Bessel-Legendre(B-L) inequalities is introduced. LKF method is used to obtain the stability criterion to ensure exponential synchronization of the system. The conservatism of the result decreases with the increase of the order of the B-L inequality. Finally, the effectiveness of the main results is verified by two simulation examples.

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