具有可变延时的四元数神经网络的指数稳定性

Exponential Stability for Quaternion-Valued Neural Networks with Time-varying Delays

研究一类具有可变延时的四元数神经网络的指数稳定性。首先将该系统分解为4个等价的实数域系统,然后在假定激活函数满足强耦合条件的情况下,利用M矩阵理论和矢量Lyapunov函数法分析该系统平衡点的全局指数稳定性,并给出了形式简单且容易验证的稳定性判据。本文所建立的稳定性条件不仅推广了现有结论,并且具有较低的保守性。最后,通过数值仿真算例验证了所得结论的正确性和低保守性。

This paper studies the exponential stability of a class of quaternion-valued neural networks with time-varying delays.The concerned quaternion-valued models were separated into four real-valued parts to form the equivalent real-valued systems.It was assumed that the activation functions were strongcoupled.Based on M-matrix properties and vector Lyapunov function method,the exponential stability of the equilibrium point of the system was analyzed,and the corresponding stability conditions were obtained for ensuring the exponential stability of the system,which was in form of compact and easy to be verified in practice.The obtained results in this paper complement the existing ones,and are the less level conservatism compared to the existing ones.Finally,a numerical example was provided to illustrate the correctness and the less level conservatism of the main results.