# Exponential Stabilization for Hybrid Recurrent Neural Networks by Delayed Noises Rooted in Discrete Observations of State and Mode

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## Abstract

Recently, the random noises derived from discrete state observations are creatively designed to realize the role of stabilization for deterministic systems in the existing result. However, for a hybrid neural network, except for the factor of discrete state observations, one always needs to consider the factors of delays and discrete mode identifications. Hence, taking delays and discrete mode identifications into account for random noises is more reasonable and practical than the original work. Motivated by the idea above, this brief is to design delayed random noises derived from discrete state observations and discrete mode identifications to almost surely exponentially stabilize an unstable hybrid recurrent neural networks, by virtue of M-matrix and stochastic analysis methods.

## Keywords

Hybrid recurrent neural networks Random noises Exponential stabilization Discrete observations Delay## Notes

### Acknowledgements

This project is partially supported by National Natural Science Foundation of China (Nos. 11571024, 61833005, 61573096 and 61272530), China Postdoctoral Science Foundation (No. 2017M621588), Science and Technology Research Foundation of Higher Education Institutions of Hebei Province of China (No. QN2017116), Graduate Foundation of North China University of Science and Technology (No. J1905), and by the Polish National Science Centre (No. 2017/27/B/ST6/02852).

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