Full Text:   <1417>

CLC number: TP183

On-line Access: 

Received: 2003-10-08

Revision Accepted: 2003-12-05

Crosschecked: 0000-00-00

Cited: 5

Clicked: 3883

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
Open peer comments

Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.1 P.32~37

http://doi.org/10.1631/jzus.2005.A0032


LMI-based approach for global asymptotic stability analysis of continuous BAM neural networks*


Author(s):  Sen-lin Zhang, Mei-qin Liu

Affiliation(s):  . School of Electrical Engineering, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   slzhang@mail.hz.zj.cn

Key Words:  Standard neural network model (SNNM), Bidirectional associative memory (BAM) neural network, Linear matrix inequality (LMI), Linear differential inclusion (LDI), Global asymptotic stability


ZHANG Sen-lin, LIU Mei-qin. LMI-based approach for global asymptotic stability analysis of continuous BAM neural networks[J]. Journal of Zhejiang University Science A, 2005, 6(1): 32~37.

@article{title="LMI-based approach for global asymptotic stability analysis of continuous BAM neural networks",
author="ZHANG Sen-lin, LIU Mei-qin",
journal="Journal of Zhejiang University Science A",
volume="6",
number="1",
pages="32~37",
year="2005",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2005.A0032"
}

%0 Journal Article
%T LMI-based approach for global asymptotic stability analysis of continuous BAM neural networks
%A ZHANG Sen-lin
%A LIU Mei-qin
%J Journal of Zhejiang University SCIENCE A
%V 6
%N 1
%P 32~37
%@ 1673-565X
%D 2005
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2005.A0032

TY - JOUR
T1 - LMI-based approach for global asymptotic stability analysis of continuous BAM neural networks
A1 - ZHANG Sen-lin
A1 - LIU Mei-qin
J0 - Journal of Zhejiang University Science A
VL - 6
IS - 1
SP - 32
EP - 37
%@ 1673-565X
Y1 - 2005
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2005.A0032


Abstract: 
Studies on the stability of the equilibrium points of continuous bidirectional associative memory (BAM) neural network have yielded many useful results. A novel neural network model called standard neural network model (SNNM) is advanced. By using state affine transformation, the BAM neural networks were converted to SNNMs. Some sufficient conditions for the global asymptotic stability of continuous BAM neural networks were derived from studies on the SNNMs’ stability. These conditions were formulated as easily verifiable linear matrix inequalities (LMIs), whose conservativeness is relatively low. The approach proposed extends the known stability results, and can also be applied to other forms of recurrent neural networks (RNNs).

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

References

[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., 1994. Linear Matrix Inequalities in System and Control Theory. , SIAM, Philadelphia, PA, 23-24. :23-24. 

[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] Fu, Y.L., Zhao, Y., Fan, Z., Liao, X.X., 2000. Bidirectional associative memory model with delays. J Huazhong Univ of Sci & Tech, (in Chinese),28(7):80-82. 

[5] Gahinet, P., Nemirovski, A., Laub, A.J., 1995. LMI Control Toolbox. , The Math Works Inc., Natick, MA, :

[6] Jing, C., 1997. Asymptotic stability of continuous bidirectional associative memory networks. Pattern Recognition and Artificial Intelligence, (in Chinese),10(1):81-86. 

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

[8] Liao, X.X., 2000. Theory and Application of Stability for Dynamical Systems, (in Chinese), National Defence Industrial Press, Beijing, China,:186-214. 

[9] 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), (in Chinese),37(1):19-23. 

[10] Moore, J.B., Anderson, B.D.O., 1968. A generalization of the Popov criterion. Journal of the Franklin Institute, 285(6):488-492. 

[11] Suykens, J.A.K., Vandewalle, J., Moor, B.D., 1998. An absolute stability criterion for the Lur’e problem with sector and slope restricted nonlinearities. IEEE Trans on Circuits and Systems-I, 45(9):1007-1009. 

[12] 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, 572-575. :572-575. 

[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. 


Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE