This paper analyzes the existing zeroing neural network (ZNN) models from the perspective of control theory. It proposes an exclusive ZNN model for solving the dynamic complex-valued matrix Moore-Penrose inverse problem: the complex-valued zeroing neural network (CVZNN). Then, a method of constructing a special type of saturation-allowed activation function is defined, which relaxes the convex constraint on the activation function when constructing the ZNN model. The convergence of the CVZNN model activated by proposed saturation-allowed functions is analyzed. Besides, the robustness of the CVZNN model under different types of noise interference is investigated based on the perspective of the control theory. Finally, the effectiveness and superiority of the CVZNN model are illustrated by simulation experiments.

本文从控制理论的角度分析了现有的归零神经网络（ZNN）模型。它提出了一个专有的ZNN模型来解决动态复数值矩阵Moore-Penrose逆问题：复数值归零神经网络（CVZNN）。然后，定义了一种构造特殊类型的饱和度允许激活函数的方法，该方法在构造ZNN模型时放宽了对激活函数的凸约束。分析了由提出的饱和度允许函数激活的CVZNN模型的收敛性。此外，基于控制理论，研究了CVZNN模型在不同类型噪声干扰下的鲁棒性。最后，通过仿真实验说明了CVZNN模型的有效性和优越性。