具有不可微时变时滞四元数神经网络的全局μ-稳定性

Global μ-stability of Quaternion-valued Neural Networks with Non-differentiable Time-varying Delays

稳定性是实值、复值、四元数神经网络在众多领域应用中首要关心的问题,针对具有不可微时变时滞的四元数神经网络的全局μ-稳定性问题,提出了在不要求网络可分解情况下的充分性判据;将四元数神经网络整体考虑,通过构造合适的Lyapunov-Krasovskii泛函,运用自由权矩阵和矩阵不等式等技术,获得了所研究网络平衡点的全局μ-稳定性的充分性条件,给出的稳定性判据是四元数线性矩阵不等式表示的,同时将所得结果与已有的结果进行了对比;最后通过一个数值仿真实例验证了结果的有效性.

Stability is the primary concern of real-valued,complex-valued,quaternion-valued neural networks in many applications.In the case where the quaternion-valued neural networks(QVNNs)with non-differential time-varying delays is not required to be separated,the sufficiency criterion of the globalμ-stability problem for networks is proposed.By constructing the appropriate Lyapunov-Krasovskii functional,using the techniques of free-weight matrix and matrix inequality,the sufficient conditions for the globalμ-stability of the equilibrium point of the network under study are obtained.The linear matrix inequalities globalμ-stability criterion is provided in the form of quaternion-valued linear matrix inequality(QVLMI).In addition,the results are compared with the existing results.Finally,a numerical example is also given to illustrate the validity and feasibility of the conclusion.