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The solving of dynamic matrix square root (DMSR) problems is frequently encountered in many scientific and engineering fields. Although the original zeroing neural network is powerful for solving the DMSR, it cannot vanish the influence of the noise perturbations, and its constant‐coefficient design scheme cannot accelerate the convergence speed. Therefore, a noise‐tolerate and adaptive coefficient zeroing neural network (NTACZNN) is raised to enhance the robust noise immunity performance and accelerate the convergence speed simultaneously. Then, the global convergence and robustness of the proposed NTACZNN are theoretically analysed under an ideal environment and noise‐perturbed circumstances. Furthermore, some illustrative simulation examples are designed and performed in order to substantiate the efficacy and advantage of the NTACZNN for the DMSR problem solution. Compared with some existing ZNNs, the proposed NTACZNN possesses advanced performance in terms of noise tolerance, solution accuracy, and convergence rate.

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The time-varying complex-valued Sylvester equation (TVCVSE) often appears in many fields such as control and communication engineering. Classical recurrent neural network (RNN) models (e.g., gradient neural network (GNN) and zeroing neural network (ZNN)) are often used to solve such problems. This paper proposes an adaptive coefficient and non-convex projection zeroing neural network (ACNPZNN) model for solving TVCVSE. To enhance its adaptability as residual error decreasing as time, an adaptive coefficient is designed based on residual error. Meanwhile, this paper breaks the convex constraint by constructing two complex-valued non-convex projection activation functions from two different aspects. Moreover, the global convergence of the proposed model is proved, the anti-noise performance of the ACNPZNN model under different noises is theoretically analyzed. Finally, simulation experiments are provided to compare the convergence performance of different models, which simultaneously verifies the effectiveness and superiority of the proposed model. INDEX TERMS Time-varying complex-valued Sylvester equation (TVCVSE), Zeroing neural network (ZNN), Adaptive coefficient, Non-convex projection.