Delay-Distribution-Dependent Stability Criteria for BAM Neural Networks with Time-Varying Delays

This paper is concerned with the delay-distributiondependent stability criteria for bidirectional associative memory (BAM) neural networks with time-varying delays. Based on the Lyapunov-Krasovskii functional and stochastic analysis approach, a delay-probability-distribution-dependent sufficient condition is derived to achieve the globally asymptotically mean square stable of the considered BAM neural networks. The criteria are formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. Finally, a numerical example and its simulation is given to demonstrate the usefulness and effectiveness of the proposed results.

Authors:

• J.H. Park
• S. Lakshmanan
• H.Y. Jung
• S.M. Lee

Keywords:

• BAM neural networks
• Probabilistic time-varying delays
• Stability criteria.

References:

[1] S. Haykin, Neural Networks: A comprehensive Foundation. NJ: Prentice
Hall 1998.
[2] A. Cichocki, R. Unbehauen, Neural networks for optimization and signal
processing. Wiley, Chichester (1993)
[3] C. Ji, H.G. Zhang, Y. Wei, "LMI Approach for Global Robust Stability
of Cohen-Grossberg Neural Networks with Multiple Delays," Neurocomputing,
vol.71, pp.475-485, 2008.
[4] T.Y. Lou, B.T. Cui, "Novel Global Stability Criteria for High-Order
Hopfield-Type Neural Networks with Time-Varying Delays," J. Math.
Anal. Appl., vol.330, pp.144-158, 2007.
[5] B. Kosko, "Bidirectional Associative Memories," IEEE Trans. Syst. Man,
Cybern. B Cybern., vol.18, pp.49-60, 1998.
[6] L. Sheng, H. Yang, "Novel Global Robust Exponential Stability Criterion
for Uncertain BAM Neural Networks with Time-Varying Delays,"
Chaos, Solitons, Fractals, vol.40, pp.2102-2113, 2009.
[7] S. Arik, "Global Asymptotic Stability Analysis of Bidirectional Associative
Memory Neural Networks with Time Delays," IEEE Trans. Neural
Netw., vol.16, pp.580-586, 2005.
[8] B. Liu, P. Shi, "Delay-Range-Dependent Stability for Fuzzy BAM
Neural Networks with Time-Varying Delays," Phy. Let. A, vol.373,
pp.1830-1838, 2009.
[9] H. Bao, J. Cao, "Delay-Distribution-Dependent State Estimation for
Discrete-Time Stochastic Neural Networks with Random Delay," Neural
Net., vol.24, pp.19-28, 2011.
[10] Y. Zhang, D. Yue, E. Tian, "Robust Delay-Distribution-Dependent Stability
of Discrete-Time Stochastic Neural Networks with Time-Varying
Delay," Neurocomputing, vol.72, pp.1265-1273, 2009.
[11] R. Yang, H. Gao, J. Lam, P. Shi, "New Stability Criteria for Neural
Networks with Distributed and Probabilistic Delays," Circ. Syst. Signal
Process, vol.28, pp.505-522, 2009.
[12] Y. Tang, J.A. Fang, M. Xia, D. Yu, "Delay-Distribution-Dependent
Stability of Stochastic Discrete-Time Neural Networks with Randomly
Mixed Time-Varying Delays," Neurocomputing, vol.72, pp.3830-3838,
2009.
[13] Y. Liu, Z. Wang, X. Liu, "Global Exponential Stability of Generalized
Recurrent Neural Networks with Discrete and Distributed Delays,"
Neural Netw., vol.19, pp.667-675, 2006.