IEEE Trans Cybern. 2020 Apr;50(4):1607-1616. doi: 10.1109/TCYB.2018.2876901. Epub 2018 Nov 9.
This paper studies one type of delayed memristor-based fractional-order neural networks (MFNNs) on the finite-time stability problem. By using the method of iteration, contracting mapping principle, the theory of differential inclusion, and set-valued mapping, a new criterion for the existence and uniqueness of the equilibrium point which is stable in finite time of considered MFNNs is established when the order α satisfies . Then, when , on the basis of generalized Gronwall inequality and Laplace transform, a sufficient condition ensuring the considered MFNNs stable in finite time is given. Ultimately, simulation examples are proposed to demonstrate the validity of the results.
本文研究了一类基于时滞忆阻器的分数阶神经网络（MFNNs）的有限时间稳定性问题。通过使用迭代法、压缩映射原理、微分包含理论和集值映射，当阶数 α 满足 时，建立了所考虑的 MFNNs 的平衡点存在且唯一且在有限时间内稳定的新准则。然后，当 时，基于广义 Gronwall 不等式和拉普拉斯变换，给出了保证所考虑的 MFNNs 在有限时间内稳定的充分条件。最后，提出了仿真示例来验证结果的有效性。
