Abstract
For a class of generalized neural networks(NNs) with discrete and distributed time-varying delays, this paper is concerned with the problem of the global exponential stability analysis. By introducing a novel augmented Lyapunov-Krasovskii functional and some appropriate free-weighting matrices, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). Finally, a numerical example is given to show the superiority of the obtained results.
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References
Cao, J., Wang, J.: Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans. Circuits Syst. I 52, 417–426 (2005)
Chen, T., Rong, L.: Delay-independent stability analysis of Cohen- Grossberg neural networks. Phys. Lett. A 317, 436–449 (2003)
Cao, J., Yuan, K., Li, H.: Global asymptotical stability of recurrent neural networks with multiple discrete delays and ditributed delays. IEEE Trans. Neural Netw. 17, 1646–1651 (2006)
Liu, Y., Wang, Z., Liu, X.: Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Networks 19, 667–675 (2006)
Li, T., Fei, S.: Exponential state estimation for recurrent nural networks with distributed delsys. Neurocomputing 71, 428–438 (2007)
Wang, Z., Liu, Y., Liu, X.: On global asymptotic stability of neural networks with discrete and distributed delays. Phys. Lett. A 345, 299–308 (2005)
Wang, Z., Shu, H., Liu, Y., Ho, D.W.C., Liu, X.: Robust stability analysis of generalized neural networks with discrete and distributed time delays. Chaos, Solitons Fractal 30, 886–896 (2006)
Liu, Y., Wang, Z., Liu, X.: Design of exponential state estimators for neural networks with mixed time delays. Phys. Lett. A 364, 401–412 (2007)
Park, J., Cho, H.: A delay-dependent asymptotic stability criterion of cellular neural networks with time-varying discrete and distributed delays. Chaos, Solitons and Fractals 33, 436–442 (2007)
He, Y., Wu, M.: Delay-dependent exponential stability of delayded neural networks with time-varying delay. IEEE Trans. Circuits Syst. 53, 553–556 (2006)
Xu, S., Lam, J.: Novel global stability criteria for interval neural networks with multiple time-varying delays. Phys. Lett. A 342, 322–330 (2005)
Liu, D., Zhang, J., Guan, X.: Exponential stability for neural networks: an LMI approach. Joural of Systems Engineering and Electronics 18, 68–71 (2007)
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Li, Q., Xing, P., wu, Y. (2010). Exponential Stability of the Neural Networks with Discrete and Distributed Time-Varying Delays. In: Zhang, L., Lu, BL., Kwok, J. (eds) Advances in Neural Networks - ISNN 2010. ISNN 2010. Lecture Notes in Computer Science, vol 6063. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13278-0_73
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DOI: https://doi.org/10.1007/978-3-642-13278-0_73
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13277-3
Online ISBN: 978-3-642-13278-0
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