CLC number: TP183
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 0000-00-00
Cited: 3
Clicked: 5809
ZHANG Jian-hai, ZHANG Sen-lin, LIU Mei-qin. Robust exponential stability analysis of a larger class of discrete-time recurrent neural networks[J]. Journal of Zhejiang University Science A, 2007, 8(12): 1912-1920.
@article{title="Robust exponential stability analysis of a larger class of discrete-time recurrent neural networks",
author="ZHANG Jian-hai, ZHANG Sen-lin, LIU Mei-qin",
journal="Journal of Zhejiang University Science A",
volume="8",
number="12",
pages="1912-1920",
year="2007",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A1912"
}
%0 Journal Article
%T Robust exponential stability analysis of a larger class of discrete-time recurrent neural networks
%A ZHANG Jian-hai
%A ZHANG Sen-lin
%A LIU Mei-qin
%J Journal of Zhejiang University SCIENCE A
%V 8
%N 12
%P 1912-1920
%@ 1673-565X
%D 2007
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2007.A1912
TY - JOUR
T1 - Robust exponential stability analysis of a larger class of discrete-time recurrent neural networks
A1 - ZHANG Jian-hai
A1 - ZHANG Sen-lin
A1 - LIU Mei-qin
J0 - Journal of Zhejiang University Science A
VL - 8
IS - 12
SP - 1912
EP - 1920
%@ 1673-565X
Y1 - 2007
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2007.A1912
Abstract: The robust exponential stability of a larger class of discrete-time recurrent neural networks (RNNs) is explored in this paper. A novel neural network model, named standard neural network model (SNNM), is introduced to provide a general framework for stability analysis of RNNs. Most of the existing RNNs can be transformed into SNNMs to be analyzed in a unified way. Applying Lyapunov stability theory method and S-Procedure technique, two useful criteria of robust exponential stability for the discrete-time SNNMs are derived. The conditions presented are formulated as linear matrix inequalities (LMIs) to be easily solved using existing efficient convex optimization techniques. An example is presented to demonstrate the transformation procedure and the effectiveness of the results.
[1] Boyd, S.P., Ghaoui, L.E., Feron, E., Balakrishnan, V., 1994. Linear Matrix Inequalities in Systems and Control Theory. SIAM. Philadelphia, PA.
[2] Cao, J.D., Wang, J., 2003. Global asymptotic stability of a general class of RNNs with time-varying delays. IEEE Trans. on Circuits & Syst.-I: Fund. Theory & Appl., 50(1):34-44.
[3] Chandrasekharan, P.C., 1996. Robust Control of Linear Dynamical Systems. Academic Press, London.
[4] Ding, K., Huang, N.J., 2006. Global robust exponential stability of interval general BAM neural networks with delays. Neural Processing Letters, 23(2):171-182.
[5] Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M., 1995. LMI Control Toolbox—For Use with Matlab. MATH Works Inc., Natick.
[6] Gau, R.S., Lien, C.H., Hsieh, J.G., 2007. Global exponential stability for uncertain cellular neural networks with multiple time-varying delays via LMI approach. Chaos, Solitons & Fractals, 32(4):1258-1267.
[7] Ji, C., Zhang, H.G., Guan, H.X., 2004. Analysis for global robust stability of Cohen-Grossberg neural networks with multiple delays. LNCS, 3173:96-101.
[8] Khargonekar, P.P., Petersen, I.R., Zhou, K., 1990. Robust stabilization of uncertain linear systems: quadratic stabilization and H( control theory. IEEE Trans. on Automatic Control, 35(3):356-361.
[9] Liang, J.L., Cao, J.D., 2006. A based-on LMI stability criterion for delayed recurrent neural networks. Chaos, Solitons & Fractals, 28(1):154-160.
[10] Liao, X.F., Chen, G.R., Sanchez, E.N., 2002. LMI-based approach for asymptotically stability analysis of delayed neural networks. IEEE Trans. on Circuits & Syst.-I: Fund. Theory & Appl., 49(7):1033-1039.
[11] Liu, M.Q., Yan, G.F., 2003. Stability analysis of recurrent multiplayer perceptrons: an LMI approach. Control Theory and Application, 20(6):292-303 (in Chinese).
[12] Liu, M.Q., 2006a. Discrete-time delayed standard neural network model and its application. Sci. China: Series F (Inf. Sci.), 49(2):137-154.
[13] Liu, M.Q., 2006b. Dynamic output feedback stabilization for nonlinear systems based on standard neural network models. Int. J. Neural Syst., 16(4):305-318.
[14] Liu, M.Q., 2007. Delayed standard neural network models for control system. IEEE Trans. on Neural Networks, 18(5):1376-1391.
[15] Ou, O., 2007. Global robust exponential stability of delayed neural networks: An LMI approach. Chaos, Solitons & Fractals, 32(5):1742-1748.
[16] Rios-Patron, E., 2000. A General Framework for the Control of Nonlinear Systems. Ph.D Thesis, University of Illinois.
[17] Singh, V., 2006. New global robust stability results for delayed cellular neural networks based on norm-bounded uncertainties. Chaos, Solitons & Fractals, 30:1165-1171.
[18] Singh, V., 2007. LMI approach to the global robust stability of a large class of neural networks with delay. Chaos, Solitons & Fractals, 32(5):1927-1934.
[19] Xie, L., de Souza, C.E., 1992. Robust H( control for linear systems with norm-bounded time-varying uncertainty. IEEE Trans. on Automatic Control, 37(8):1188-1191.
[20] Yan, G.F., Zhang, S.L., Liu, M.Q., 2004. Standard neural network model and its applications. J. Zhejiang Univ. (Eng. Sci.), 38(3):298-301 (in Chinese).
[21] Zeng, Z.G., Wang, J., Liao, X.X., 2005. Global asymptotic stability and global exponential stability of neural networks with unbounded time-varying delays. IEEE Trans. on Circuits & Syst.-II: Express Briefs, 52(3):168-173.
[22] Zhang, S.L., Liu, M.Q., 2005. LMI-based approach for global asymptotical stability analysis of continuous BAM neural networks. J. Zhejiang Univ. Sci., 6A(1):32-37.
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