Novel Inequalities to Global Mittag–Leffler Synchronization and Stability Analysis of Fractional-Order Quaternion-Valued Neural Networks
Novel Inequalities to Global Mittag–Leffler Synchronization and Stability Analysis of Fractional-Order Quaternion-Valued Neural Networks
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DOI：
10.1109/tnnls.2020.3015952
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发表时间：
2020-09
影响因子：
10.4
通讯作者：
Jianying Xiao;Jinde Cao;Jun Cheng;S. Wen;Ruimei Zhang;S. Zhong
中科院分区：
文献类型：
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作者：
Jianying Xiao;Jinde Cao;Jun Cheng;S. Wen;Ruimei Zhang;S. Zhong
研究分数阶四元数值神经网络的全局Mittag-Leffler同步和稳定性问题。成功地建立了包含一般激活函数和线性阈值激活函数的FOQVNN系统。同时，两种不同的方法，如分离和非分离，已被用来解决所研究的FOQVNNs系统的转换，这不满足四元数乘法的交换性。此外，基于一般参数，得到了两个新的不等式。与已有的不等式相比，新的不等式由于可以充分利用附加参数而具有独特的优越性。利用李雅普诺夫理论，可以构造出两个新的李雅普诺夫-克拉索夫斯基泛函（LKF）. LKF的新奇来自于更广泛的参数，这些参数可以参与LKF的构建。此外，主要是基于新的不等式和LKF，更多的和更灵活的准则，有效地获得所讨论的问题。最后，给出了四个数值例子来证明所推导准则的相关有效性和可用性。
This article is concerned with the problem of the global Mittag–Leffler synchronization and stability for fractional-order quaternion-valued neural networks (FOQVNNs). The systems of FOQVNNs, which contain either general activation functions or linear threshold ones, are successfully established. Meanwhile, two distinct methods, such as separation and nonseparation, have been employed to solve the transformation of the studied systems of FOQVNNs, which dissatisfy the commutativity of quaternion multiplication. Moreover, two novel inequalities are deduced based on the general parameters. Compared with the existing inequalities, the new inequalities have their unique superiorities because they can make full use of the additional parameters. Due to the Lyapunov theory, two novel Lyapunov–Krasovskii functionals (LKFs) can be easily constructed. The novelty of LKFs comes from a wider range of parameters, which can be involved in the construction of LKFs. Furthermore, mainly based on the new inequalities and LKFs, more multiple and more flexible criteria are efficiently obtained for the discussed problem. Finally, four numerical examples are given to demonstrate the related effectiveness and availability of the derived criteria.