Liu Yurong, Wang Zidong, Liu Xiaohui
Department of Mathematics, Yangzhou University, Yangzhou 225002, PR China.
Neural Netw. 2009 Jan;22(1):67-74. doi: 10.1016/j.neunet.2008.10.001. Epub 2008 Oct 18.
This paper is concerned with the stability analysis problem for a new class of discrete-time recurrent neural networks with mixed time-delays. The mixed time-delays that consist of both the discrete and distributed time-delays are addressed, for the first time, when analyzing the asymptotic stability for discrete-time neural networks. The activation functions are not required to be differentiable or strictly monotonic. The existence of the equilibrium point is first proved under mild conditions. By constructing a new Lyapnuov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the discrete-time neural networks to be globally asymptotically stable. As an extension, we further consider the stability analysis problem for the same class of neural networks but with state-dependent stochastic disturbances. All the conditions obtained are expressed in terms of LMIs whose feasibility can be easily checked by using the numerically efficient Matlab LMI Toolbox. A simulation example is presented to show the usefulness of the derived LMI-based stability condition.
本文关注一类具有混合时滞的新型离散时间递归神经网络的稳定性分析问题。在分析离散时间神经网络的渐近稳定性时，首次考虑了由离散时滞和分布时滞组成的混合时滞。激活函数不要求可微或严格单调。首先在温和条件下证明了平衡点的存在性。通过构造一个新的Lyapnuov-Krasovskii泛函，发展了一种线性矩阵不等式（LMI）方法来建立离散时间神经网络全局渐近稳定的充分条件。作为扩展，我们进一步考虑同一类神经网络但具有状态依赖随机干扰的稳定性分析问题。所得到的所有条件都以LMI的形式表示，其可行性可以通过使用数值高效的Matlab LMI工具箱轻松检验。给出了一个仿真例子以说明基于LMI的稳定性条件的有效性。
