A Triple Noise Tolerant Zeroing Neural Network for Time-Varing Matrix Inverse

Matrix inversion is a fundamental operation utilized across numerous disciplines such as mathematics, engineering, and control theory. The original zeroing neural network (OZNN) method has proven effective in tackling the challenge of time-varying matrix inversion (TVMI) under ideal conditions. The integration-enhanced zeroing neural network (IEZNN) is commonly used to handle TVMI issues in the presence of various types of noise. In this paper, we have enhanced the IEZNN model's tolerance to noise by introducing a dual integral component, resulting in the dual noise tolerant zeroing neural network (DNTZNN) model. We have further improved this model by incorporating a positive odd activation function to create the triple noise tolerant zeroing neural network (TNTZNN). This advancement enables the TNTZNN to effectively solve TVMI problems despite various noise disturbances. Consequently, the TNTZNN model demonstrates excellent convergence and robustness even under noisy conditions. Furthermore, theoretical analysis grounded on the Lyapunov theorem validates the convergence and resilience of the TNTZNN model against diverse forms of noise. Computational simulations further substantiate the superior efficacy of the proposed TNTZNN model in resolving TVMI problems.