Robust Stability Analysis of a Class of Delayed Neural Networks
Neyir Ozcan, Sabri Arik
2012
Abstract
This paper studies the global robust stability of delayed neural networks. A new sufficient condition that ensures the existence, uniqueness and global robust asymptotic stability of the equilibrium point is presented. The obtained condition is derived by using the Lyapunov stability and Homomorphic mapping theorems and by employing the Lipschitz activation functions. The result presented establishes a relationship between the network parameters of the neural system independently of time delays. We show that our results is new and improves some of the previous global robust stability results expressed for delayed neural networks.
References
- Arik, S. and Tavsanoglu, V. (2000). On the global asymptotic stability of delayed cellular neural networks. IEEE Trans. Circuits and Syst.I, 47(5):571-574.
- Cao, J. and Wang, J. (2003). Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. Circuits and Syst.I, 50:34-44.
- Cao, J. and Wang, J. (2005). Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans. Circuits and Syst.I, 52:417-426.
- Ensari, T. and Arik, S. (2010). New results for robust stability of dynamical neural networks with discrete time delays. Expert Systems with Applications, 27:5925- 5930.
- Forti, M. and Tesi, A. (1995). New conditions for global stability of neural networks with applications to linear and quadratic programming problems. IEEE Trans. Circuits Syst., 42(7):354-365.
- Li, X. M., Huand, L. H., and Zhu, H. (2003). Global stability of cellular neural networks with constant and variable delays. Nonlinear Analysis, 53:319-333.
- Liao, T.-L. and Wang, F. C. (2000). Global stability for cellular neural networks with time delay. IEEE Trans. on Neural Networks, 11:1481-1485.
- Liao, X., Chen, G., and Sanchez, E. N. (2002). Lmi-based approach for asymptotic stability analysis ofdelayed neural networks. IEEE Trans. Circuits and Syst.I, 49:1033-1039.
- Liao, X. F., Wong, K. W., Wu, Z., and Chen, G. (2001). Novel robust stability for interval-delayed hopfield neural. IEEE Trans. Circuits and Syst.I, 48:1355- 1359.
- Liao, X. F. and Yu, J. (1998). Robust stability for interval hopfield neural networks with time delay. IEEE Trans. Neural Networks, 9:1042-1045.
- Mohamad, S. (2001). Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks. Physica D, 159:233-251.
- Ozcan, N. and Arik, S. (2006). Global robust stability analysis of neural networks with multiple time delays. IEEE Trans. Circuits and Syst.I, 53(1):166-176.
- Singh, V. (2007). Global robuststability of delayed neural networks: Estimating upper limit of norm of delayed connection weight matrix. Chaos, Solitons and Fractals, 32:259263.
- Sun, C. and Feng, C. B. (2003). Global robust exponential stability of interval neural networks with delays. Neural Processing Letters, 17:107-115.
- Wang, K. and Michel, A. N. (1996). On the stability of family of nonlinear time varying systems. IEEE Trans. Circuits Syst., 43(7):517-531.
- Yi, Z. and Tan, K. (2002). Dynamicstability conditions for lotka-volterra recurrent neural networks with delays. hysical Review E, 66:011910.
Paper Citation
in Harvard Style
Ozcan N. and Arik S. (2012). Robust Stability Analysis of a Class of Delayed Neural Networks . In Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: NCTA, (IJCCI 2012) ISBN 978-989-8565-33-4, pages 603-606. DOI: 10.5220/0004090506030606
in Bibtex Style
@conference{ncta12,
author={Neyir Ozcan and Sabri Arik},
title={Robust Stability Analysis of a Class of Delayed Neural Networks},
booktitle={Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: NCTA, (IJCCI 2012)},
year={2012},
pages={603-606},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004090506030606},
isbn={978-989-8565-33-4},
}
in EndNote Style
TY - CONF
JO - Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: NCTA, (IJCCI 2012)
TI - Robust Stability Analysis of a Class of Delayed Neural Networks
SN - 978-989-8565-33-4
AU - Ozcan N.
AU - Arik S.
PY - 2012
SP - 603
EP - 606
DO - 10.5220/0004090506030606