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Complex-valued time-dependent matrix inversion (TDMI) is extensively exploited in practical industrial and engineering fields. Many current neural models are presented to find the inverse of a matrix in an ideal noise-free environment. However, the outer interferences are normally believed to be ubiquitous and avoidable in practice. If these neural models are applied to complex-valued TDMI in a noise environment, they need take a lot of precious time to deal with outer noise disturbances in advance. Thus, a noise-suppression model is urgent to be proposed to address this problem. In this study, a complex-valued noise-tolerant zeroing neural network (CVNTZNN) on the basis of an integral-type design formula is established and investigated for finding complex-valued TDMI under a wide variety of noises. Furthermore, both convergence and robustness of the CVNTZNN model are carefully analyzed and rigorously proved. For comparison and verification purposes, the existing zeroing neural network (ZNN) and gradient neural network (GNN) have been presented to address the same problem under the same conditions. Numerical simulation consequences demonstrate the effectiveness and excellence of the proposed CVNTZNN model for complex-valued TDMI under various kinds of noises, by comparing the existing ZNN and GNN models.

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Different from the traditional linearly activated gradient-based neural network model (GNN model), two nonlinear activation functions are presented and investigated to construct two nonlinear gradient-based neural network models (NGNN-1 model and NGNN-2 model) for matrix inversion in this paper. For comparative and illustrative purposes, the traditional GNN model is also used to solve matrix inversion problems under the same circumstance. In addition, the simulation results of the computer finally confirm the validity and superiority of the two nonlinear gradient-based neural network models specially activated by two nonlinear activation functions for matrix inversion, as compared with the traditional GNN model.