一类复值神经网络的随机指数鲁棒稳定性

Stochastic Exponential Robust Stability of a Class of Complex-Valued Neural Networks

  • 摘要: 为分析Markova跳变参数对系统的影响,研究了一类具有Markova跳变参数和变时滞的复数域区间神经网络的动态行为。在假定复数域激活函数仅满足Lipchitz条件的情况下,首先利用M矩阵理论和同胚映射相关原理,研究了该系统平衡点的存在性和唯一性。然后利用矢量Lyapunov函数法分析了不同模式下平衡点的随机指数鲁棒稳定性。建立的稳定性条件推广了现有结论,并且容易验证。最后,通过一个数值仿真算例验证了所得结论的可行性。

     

    Abstract: In order to analyze the influence of the Markova jumping parameters on the system, this paper deals with dynamic behavior analysis for a class of interval neural networks defined in complex number domain with Markova jumping parameters and time-varying delays. It is assumed that the activation functions defined in complex number domain satisfy Lipschitz condition. Firstly, the existence and uniqueness of the equilibrium point of the addressed system are studied by employing the M-matrix theory and the homeomorphism mapping theory. Then, the stochastic exponential robust stability of the equilibrium point is analyzed based on the idea of the vector Lyapunov function method. The presented stability analysis is the generalization of existing ones not only, but also easy to be verified in the practice applications. Finally, a numerical example with several simulation results is given to illustrate the feasibility of the obtained results in this paper.

     

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