LMI conditions for global stability of fractional-order neural networks
LMI conditions for global stability of fractional-order neural networks
复制标题
分数阶神经网络全局稳定性的 LMI 条件
DOI：
10.1109/tnnls.2016.2574842
复制
发表时间：
2017
影响因子：
10.4
通讯作者：
Junzhi Yu
中科院分区：
文献类型：
--
作者：
Shuo Zhang;Yongguang Yu;Junzhi Yu
分数阶神经网络在神经元相互作用的信息处理建模中起着至关重要的作用。分数阶神经网络的全局稳定性研究仍然是一个开放而必要的课题。本文提出了分数阶线性和非线性系统的简化线性矩阵不等式稳定性条件。然后，利用得到的LMI条件对分数阶神经网络进行全局稳定性分析。在LMI形式下，得到的结果包括平衡点的存在唯一性及其全局稳定性，简化和推广了以往关于分数阶神经网络稳定性分析的一些工作。在此基础上，给出了这类神经系统间的广义投影同步方法，并给出了相应的LMI条件。最后，给出了两个数值算例来说明所建立的LMI条件的有效性。
Fractional-order neural networks play a vital role in modeling the information processing of neuronal interactions. It is still an open and necessary topic for fractional-order neural networks to investigate their global stability. This paper proposes some simplified linear matrix inequality (LMI) stability conditions for fractional-order linear and nonlinear systems. Then, the global stability analysis of fractional-order neural networks employs the results from the obtained LMI conditions. In the LMI form, the obtained results include the existence and uniqueness of equilibrium point and its global stability, which simplify and extend some previous work on the stability analysis of the fractional-order neural networks. Moreover, a generalized projective synchronization method between such neural systems is given, along with its corresponding LMI condition. Finally, two numerical examples are provided to illustrate the effectiveness of the established LMI conditions.