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Robust exponential stability of uncertain fuzzy Cohen-Grossberg neural networks with time-varying delays. (English) Zbl 1185.68511
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.
MSC:
68T05Learning and adaptive systems
93C42Fuzzy control systems
93D05Lyapunov and other classical stabilities of control systems
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 · doi:10.1016/j.physleta.2005.04.095
[2]Boyd, B.; Ghoui, L. E.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in system and control theory, (1994)
[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 · doi:10.1016/S0165-0114(00)00120-2
[4]Cao, J.; Li, X.: Stability in delayed Cohen – Grossberg neural networks: LMI optimization approach, Physica D 212, 54-65 (2005) · Zbl 1097.34053 · doi:10.1016/j.physd.2005.09.005
[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 · doi:10.1016/j.physleta.2003.08.066
[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 · doi:10.1016/j.chaos.2004.05.029
[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 · doi:10.1016/S0005-1098(99)00025-4
[10]P. Gahinet, A. Nemirovski, A. Laub, M. Chilali, LMI Control Toolbox User’s Guide, The Mathworks, Massachusetts, 1995.
[11]Gu, K.; Kharitonov, V. L.; Chen, J.: Stability of time delay systems, (2003)
[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, No. 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 · doi:10.1016/j.physleta.2003.10.002
[15]Ji, C.; Zhang, H. G.: Robust stability of time-delayed Hopfield neural networks with parameter perturbations, Acta electron. Sin. 33, 115-118 (2005)
[16]C. Ji, H.G. Zhang, LMI Approach to robust stability analysis of Hopfield neural networks, in: Proc. of 16th IFAC World Congress, Prague, Czech, 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)
[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 · doi:10.1016/j.fss.2007.07.015
[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 · doi:10.1162/089976603765202703
[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 · doi:10.1016/S0167-2789(00)00134-2
[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]Ali, M. Syed; 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 · doi:10.1016/j.physleta.2008.05.067
[27]Ali, M. Syed; Balasubramaniam, P.: Robust stability of uncertain fuzzy Cohen Grossberg BAM neural networks with time-varying delays, Expert syst. Appl. 36, 10583-10588 (2009)
[28]Ali, M. Syed; 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 · doi:10.1016/j.chaos.2009.03.138
[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) · Zbl 0758.93042 · doi:10.1016/0165-0114(92)90113-I
[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 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 · doi:10.1016/0304-3975(95)00085-2
[34]Wang, L.; Zou, X.: Harmless delays in Cohen – Grossberg neural networks, Physica D 170, 162-173 (2002) · Zbl 1025.92002 · doi:10.1016/S0167-2789(02)00544-4
[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, No. 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)
[38]J. Zhang, D. Ren, W. Zhang, Global exponential stability of fuzzy Cohen – Grossberg neural networks with variable delays and distributed delays, in: Lecture Notes in Computer Science, Springer, Berlin, 2007, pp. 66 – 74.