Similar articles

Abstract: To facilitate stability analysis of discrete-time bidirectional associative memory (BAM) neural networks, they were converted into novel neural network models, termed standard neural network models (SNNMs), which interconnect linear dynamic systems and bounded static nonlinear operators. By combining a number of different Lyapunov functionals with S-procedure, some useful criteria of global asymptotic stability and global exponential stability of the equilibrium points of SNNMs were derived. These stability conditions were formulated as linear matrix inequalities (LMIs). So global stability of the discrete-time BAM neural networks could be analyzed by using the stability results of the SNNMs. Compared to the existing stability analysis methods, the proposed approach is easy to implement, less conservative, and is applicable to other recurrent neural networks.

[1] Barabanov, N.E., Prokhorov, D.V., 2002. Stability analysis of discrete-time recurrent neural networks. IEEE Trans. on Neural Networks, 13(2):292-303.

[2] Boyd, S.P., Ghaoui, L.E., Feron, E., Balakrishnan, V., 1994. Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia, PA.

[3] Cao, J.D., Wang, L., 2002. Exponential stability and periodic oscillatory solution in BAM networks with delays. IEEE Trans. on Neural Networks, 13(2):457-463.

[4] Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M., 1995. LMI Control Toolbox−For Use with Matlab. The Math Works Inc., Natick, MA.

[5] Jin, C., 1999. Stability analysis of discrete-time Hopfield BAM neural networks. Acta Automatica Sinica, 25(5):606-612 (in Chinese).

[6] Kosko, B., 1987. Adaptive bidirectional associative memories. Appl. Opt., 26(23):4947-4960.

[7] Liu, M.Q., Zhang, S.L., 2003. Stability analysis of a class of discrete-time recurrent neural networks: an LMI approach. Journal of Zhejiang University (Engineering Science), 37(1):19-23 (in Chinese).

[8] Smart, D.R., 1980. Fixed Point Theorems. Cambridge University Press, Cambridge.

[9] Wang, C.C., Don, H.S., 1995. An analysis of high-capacity discrete exponential BAM. IEEE Trans. on Neural Networks, 6(2):492-496.

[10] Xu, B.Z., Zhang, B.L., Kwong, C.P., 1992. Asymptotic Stability Analysis of Continuous Bidirectional Associative Memory Networks. IEEE International Conference on Systems Engineering, Kobe, Japan, p.572-575.

[11] Xu, Z.X., Zheng, C.Y., Ye, Z., Xie, M.P., 1999. Complex-valued multistate bidirectional associative memory. Acta Electronica Sinica, 27(5):118-120 (in Chinese).

[12] Zhang, S.L., Liu, M.Q., 2005. LMI-based approach for global asymptotical stability analysis of continuous BAM neural networks. Journal of Zhejiang University SCIENCE, 6A(1):32-37.

[13] Zhang, B.L., Xu, B.Z., Kwong, P.K., 1993. Performance analysis of the bidirectional associative memory and an improved model from the matched-filtering viewpoint. IEEE Trans. on Neural Networks, 4(5):864-872.