Jian Jigui, Wan Peng
College of Science, China Three Gorges University, Yichang, Hubei, 443002, China.
Neural Netw. 2017 Jul;91:1-10. doi: 10.1016/j.neunet.2017.03.011. Epub 2017 Apr 12.
This paper deals with the problem on Lagrange α-exponential stability and α-exponential convergence for a class of fractional-order complex-valued neural networks. To this end, some new fractional-order differential inequalities are established, which improve and generalize previously known criteria. By using the new inequalities and coupling with the Lyapunov method, some effective criteria are derived to guarantee Lagrange α-exponential stability and α-exponential convergence of the addressed network. Moreover, the framework of the α-exponential convergence ball is also given, where the convergence rate is related to the parameters and the order of differential of the system. These results here, which the existence and uniqueness of the equilibrium points need not to be considered, generalize and improve the earlier publications and can be applied to monostable and multistable fractional-order complex-valued neural networks. Finally, one example with numerical simulations is given to show the effectiveness of the obtained results.
本文研究了一类分数阶复值神经网络的拉格朗日α - 指数稳定性和α - 指数收敛性问题。为此，建立了一些新的分数阶微分不等式，改进并推广了先前已知的准则。通过使用这些新不等式并结合李雅普诺夫方法，推导了一些有效准则以保证所研究网络的拉格朗日α - 指数稳定性和α - 指数收敛性。此外，还给出了α - 指数收敛球的框架，其中收敛速率与系统的参数和微分阶数有关。这里的这些结果，无需考虑平衡点的存在性和唯一性，推广并改进了早期的出版物，可应用于单稳态和多稳态分数阶复值神经网络。最后，给出了一个带有数值模拟的例子以说明所得结果的有效性。
