×
Balasubramaniam, P.; Ali, M. Syed

Robust exponential stability of uncertain fuzzy Cohen-Grossberg neural networks with time-varying delays. (English) Zbl 1185.68511

Fuzzy Sets Syst. 161, No. 4, 608-618 (2010).
Summary: In this paper, the Takagi-Sugeno (T-S) fuzzy model representation is extended to the stability analysis for uncertain Cohen-Grossberg neural networks (CGNNs) with time-varying delays. A novel linear matrix inequality based stability criterion is obtained by using Lyapunov functional theory to guarantee the exponential stability of uncertain CGNNs with time varying delays which are represented by T-S fuzzy models. Finally, the proposed stability conditions are demonstrated with numerical examples.

Cited in 18 Documents

MSC:

68T05 Learning and adaptive systems in artificial intelligence
93C42 Fuzzy control/observation systems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory

Keywords:

Cohen-Grossberg neural networks; global exponential stability; linear matrix inequality; Lyapunov functional; time-varying delays; T-S fuzzy model

Software:

LMI toolbox
PDF BibTeX XML Cite
\textit{P. Balasubramaniam} and \textit{M. S. Ali}, Fuzzy Sets Syst. 161, No. 4, 608--618 (2010; Zbl 1185.68511)
Full Text: DOI

References:

[1] Arik, S.; Orman, Z., Global stability analysis of Cohen-Grossberg neural networks with time varying delays, Phys. Lett. A, 341, 410-421 (2005) · Zbl 1171.37337
[2] Boyd, B.; Ghoui, L. E.; Feron, E.; Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory (1994), SIAM: SIAM Philadelphia, PA
[3] Cao, Y. Y.; Frank, P. M., Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models, Fuzzy Sets and Systems, 124, 213-229 (2001) · Zbl 1002.93051
[4] Cao, J.; Li, X., Stability in delayed Cohen-Grossberg neural networks: LMI optimization approach, Physica D, 212, 54-65 (2005) · Zbl 1097.34053
[5] Cao, J.; Yuan, K.; Li, H. X., Global asymptotic stability of recurrent neural networks with multiple discrete delays and distributed delays, IEEE Trans. Neural Networks, 17, 1646-1651 (2006)
[6] Chen, T. P.; Rong, L. B., Delay-independent stability analysis of Cohen-Grossberg neural networks, Phys. Lett. A, 317, 436-449 (2003) · Zbl 1030.92002
[7] Chen, A.; Cao, J.; Huang, L., Global robust stability of interval cellular neural networks with time varying delays, Chaos Solitons Fractals, 23, 787-799 (2005) · Zbl 1101.68752
[8] Cohen, M. A.; Grossberg, S., Absolute stability of global pattern formation and parallel memory storage by competitive neural networks, IEEE Trans. Syst. Man Cybern., 13, 815-826 (1983) · Zbl 0553.92009
[9] De Souza, C. E.; Li, X., Delay-dependent robust control of uncertain linear state-delayed systems, Automatica, 35, 1313-1321 (1999) · Zbl 1041.93515
[11] Gu, K.; Kharitonov, V. L.; Chen, J., Stability of Time Delay Systems (2003), Birkhäuser: Birkhäuser Boston · Zbl 1039.34067
[12] Huang, H.; Ho, D. W.C.; Lam, J., Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays, IEEE Trans. Circ. Syst. II, 52, 251-255 (2005)
[13] Huang, H.; Ho, D. W.C., Delay-dependent robust control of uncertain stochastic fuzzy systems with time-varying delay, IET Control Theory Appl., 1, 4, 1075-1085 (2007)
[14] Huang, C. C.; Cheng, C. J.; Liao, T. L., Globally exponential stability of generalized Cohen-Grossberg neural networks with delays, Phys. Lett. A, 319, 157-166 (2003) · Zbl 1073.82597
[15] Ji, C.; Zhang, H. G., Robust stability of time-delayed Hopfield neural networks with parameter perturbations, Acta Electron. Sin., 33, 115-118 (2005)
[17] Ji, C.; Zhang, H. G.; Wang, Z. S., Dynamic analysis for the generalized neural networks with time delay and asymmetric structure, Control Decision, 19, 1416-1419 (2004) · Zbl 1095.34551
[18] Liao, X.; Chen, G.; Sanchez, E. N., LMI-based for asymptotically stability analysis of delayed neural networks, IEEE Trans. Circ. Syst. I, 49, 1033-1039 (2002) · Zbl 1368.93598
[19] Lin, F. J.; Lin, C. H., On line gain tuning IP controller using RFNN, IEEE Trans. AeroSpace Electron. Syst., 37, 655-670 (2001)
[20] Lou, X.; Cui, B., Robust asymptotic stability of uncertain fuzzy BAM neural networks with time-varying delays, Fuzzy Sets and Systems, 158, 2746-2756 (2007) · Zbl 1133.93366
[21] Lu, W.; Chen, T. P., New conditions on global stability of Cohen-Grossberg neural networks, Neural Comput., 15, 1173-1189 (2003) · Zbl 1086.68573
[22] Otto, M.; George, T.; Schierle, C.; Wegscheilder, W., Fuzzy logic and neural networks—applications to analytic chemistry, Pure Appl. Chem., 64, 497-502 (1992)
[23] Shitonga, W.; Duana, F.; Mina, X.; Dewenc, H., Advanced fuzzy cellular neural network: application to CT liver images, Artif. Intell. Med., 39, 65-77 (2007)
[24] Shih, C. W.; Weng, C. W., Cycle-symmetric matrices and convergent neural networks, Physica D, 146, 213-220 (2000) · Zbl 0986.92004
[25] Song, Q.; Cao, J., Impulsive effects on stability of fuzzy Cohen-Grossberg neural networks with time-varying delays, IEEE Trans. Syst. Man Cybern., 37, 733-741 (2007)
[26] Syed Ali, M.; Balasubramaniam, P., Robust stability of uncertain stochastic fuzzy BAM neural networks with time varying delay, Phys. Lett. A, 372, 5159-5166 (2008) · Zbl 1221.34190
[27] Syed Ali, M.; Balasubramaniam, P., Robust stability of uncertain fuzzy Cohen Grossberg BAM neural networks with time-varying delays, Expert Syst. Appl., 36, 10583-10588 (2009)
[28] Syed Ali, M.; Balasubramaniam, P., Global exponential stability of uncertain fuzzy BAM neural networks with time-varying delays, Chaos Solitons Fractals, 42, 2191-2199 (2009) · Zbl 1198.93192
[29] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst. Man Cybern., 15, 116-132 (1985) · Zbl 0576.93021
[30] Takagi, T.; Sugeno, M., Stability analysis and design of fuzzy control systems, Fuzzy Sets and Systems, 45, 135-156 (1993)
[31] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modelling and control, IEEE Trans. Syst. Man Cybern., 15, 116-132 (1985) · Zbl 0576.93021
[32] Tanaka, K.; Ikede, T.; Wang, H. O., Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, \(H^\infty\) control theory, and linear matrix inequalities, IEEE Trans. Fuzzy Syst., 4, 1-13 (1996)
[33] Takahashi, Y., Solving optimization problems with variable-constraint by an extended Cohen-Grossberg model, Theor. Comput. Sci., 158, 279-341 (1996) · Zbl 0871.68148
[34] Wang, L.; Zou, X., Harmless delays in Cohen-Grossberg neural networks, Physica D, 170, 162-173 (2002) · Zbl 1025.92002
[35] Wang, Z.; Ho, D. W.C.; Liu, X., A note on the robust stability of uncertain stochastic fuzzy systems with time-delays, IEEE Trans. Syst. Man Cybern. Part A, 34, 4, 570-576 (2004)
[36] Ye, H.; Michel, A. N.; Wang, K., Analysis of Cohen-Grossberg neural networks with multiple delays, Phys. Rev. E, 51, 2611-2618 (1995)
[37] Yuan, K.; Cao, J.; Li, H. X., Robust stability of switched Cohen-Grossberg neural networks with mixed time-varying delays, IEEE Trans. Syst. Man Cybern. Part B, 36, 1356-1363 (2006)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.