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Global asymptotic and robust stability of recurrent neural networks with time delays
Abstract
In this paper, two related problems, global asymptotic stability (GAS) and global robust stability (GRS) of neural networks with time delays, are studied. First, GAS of delayed neural networks is discussed based on Lyapunov method and linear matrix inequality. New criteria are given to ascertain the GAS of delayed neural networks. In the designs and applications of neural networks, it is necessary to consider the deviation effects of bounded perturbations of network parameters. In this case, a delayed neural network must be formulated as a interval neural network model. Several sufficient conditions are derived for the existence, uniqueness, and GRS of equilibria for interval neural networks with time delays by use of a new Lyapunov function and matrix inequality. These results are less restrictive than those given in the earlier references.
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Hopfield, J. J. (1984) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.81.10.3088 · Cited by 6,918
Cited by
Extended Dissipative State Estimation for Markov Jump Neural Networks With Unreliable Links
Shen, H., Zhu, Y., Zhang, L., & Park, J. H. (2017) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2015.2511196 · Cited by 489
Exponential stability analysis of memristor-based recurrent neural networks with time-varying delays
Wen, S., Zeng, Z., & Huang, T. (2012) · Neurocomputing · doi:10.1016/j.neucom.2012.06.014 · Cited by 184
Metadata
- Authors
- Cao, J., & Wang, J.
- Venue
- IEEE Transactions on Circuits and Systems I: Regular Papers
- Published
- 2005-02
- Volume
- 52
- Issue
- 2
- Pages
- 417-426
- ISSN
- 1057-7122 (ISSN-L)
- OpenAlex
- W2108517517
- Cited by
- 491
- References
- 1
- FWCI
- 64.57
- Type
- journal article
- Language
- en
- Open access
- closed
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- Cao, J., & Wang, J. (2005). Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Transactions on Circuits and Systems I: Regular Papers. https://doi.org/10.1109/tcsi.2004.841574
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