# A finite-time convergent Zhang neural network and its application to real-time matrix square root finding

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## Abstract

In this paper, a finite-time convergent Zhang neural network (ZNN) is proposed and studied for matrix square root finding. Compared to the original ZNN (OZNN) model, the finite-time convergent ZNN (FTCZNN) model fully utilizes a nonlinearly activated sign-bi-power function, and thus possesses faster convergence ability. In addition, the upper bound of convergence time for the FTCZNN model is theoretically derived and estimated by solving differential inequalities. Simulative comparisons are further conducted between the OZNN model and the FTCZNN model under the same conditions. The results validate the effectiveness and superiority of the FTCZNN model for matrix square root finding.

## Keywords

Zhang neural networks Matrix square root Finite-time convergence Nonlinear activation function Upper bound## Notes

### Acknowledgements

This work is supported by the Natural Science Foundation of Hunan Province, China (grant no. 2016JJ2101), the National Natural Science Foundation of China (grant no. 61503152), the Research Foundation of Education Bureau of Hunan Province, China (grant no. 15B192), the National Natural Science Foundation of China (grant nos. 61563017, 61561022, 61363073, and 61363033), and the Research Foundation of Jishou University, China (grant nos. 2015SYJG034, JGY201643, and JG201615). In addition, the author thanks the editors and anonymous reviewers for their valuable suggestions and constructive comments which have really helped the author improve the presentation and quality of this paper very much.

### Compliance with ethical standards

### Conflict of interests

The author declares that he has no conflict of interest.

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