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A new stability analysis of delayed cellular neural networks. (English) Zbl 1154.34386
Summary: The global asymptotic stability of delayed cellular neural networks (DCNNs) is investigated. A novel criterion for the stability using the Lyapunov stability theory and linear matrix inequality (LMI) framework is presented. The criterion expressed by LMIs is delay-dependent. The result is less conservative than those established in the earlier references. A numerical example is given to show the effectiveness of proposed method.

MSC:
34K20Stability theory of functional-differential equations
92B20General theory of neural networks (mathematical biology)
Software:
LMI toolbox
WorldCat.org
Full Text: DOI
References:
[1] Chua, L.; Yang, L.: Cellular neural networks: theory and applications. IEEE trans. Circ. syst. I 35, 1257-1290 (1988) · Zbl 0663.94022
[2] Ramesh, M.; Narayanan, S.: Chaos control of bonhoeffer-van der Pol oscillator using neural networks. Chaos solitons fract. 12, 2395-2405 (2001) · Zbl 1004.37067
[3] Chen, C. J.; Liao, T. L.; Hwang, C. C.: Exponential synchronization of a class of chaotic neural networks. Chaos solitons fract. 24, 197-206 (2005) · Zbl 1060.93519
[4] Otawara, K.; Fan, L. T.; Tsutsumi, A.; Yano, T.; Kuramoto, K.; Yoshida, K.: An artificial neural network as a model for chaotic behavior of a three-phase fluidized bed. Chaos solitons fract. 13, 353-362 (2002) · Zbl 1073.76656
[5] Cannas, B.; Cincotti, S.; Marchesi, M.; Pilo, F.: Learning of Chua’s circuit attractors by locally recurrent neural networks. Chaos solitons fract. 12, 2109-2115 (2001) · Zbl 0981.68135
[6] Cao, J.: Global asymptotic stability of neural networks with transmission delays. Int. J. Syst. sci. 31, 1313-1316 (2000) · Zbl 1080.93517
[7] Chen, A.; Cao, J.; Huang, L.: An estimation of upperbound of delays for global asymptotic stability of delayed Hopfield neural networks. IEEE trans. Circ. syst. I 49, 1028-1032 (2002)
[8] Arik, S.; Tavsanoglu, V.: On the global asymptotic stability of delayed cellular neural networks. IEEE trans. Circ. syst. Part I: fundam. Theory appl. 47, 571-574 (2000) · Zbl 0997.90095
[9] Liao, T. L.; Wang, F. C.: Global stability for cellular neural networks with time delay. IEEE trans. Neural network 11, 1481-1484 (2000)
[10] Cao, J.: Global stability conditions for delayed cnns. IEEE trans. Circ. syst. I 48, 1330-1333 (2001) · Zbl 1006.34070
[11] Arik, S.: An analysis of global asymptotic stability of delayed cellular neural networks. IEEE trans. Neural network 13, 1239-1242 (2002)
[12] Arik, S.: An improved global stability result for delayed cellular neural networks. IEEE trans. Circ. syst. I 49, 1211-1214 (2002)
[13] Singh, V.: Robust stability of cellular neural networks with delay: linear matrix inequality approach. IEEE proc. Control theory appl. 151, 125-129 (2004)
[14] Boyd, B.; Ghaoui, L. E.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in systems and control theory. (1994) · Zbl 0816.93004
[15] Gahinet, P.; Nemirovski, A.; Laub, A.; Chilali, M.: LMI control toolbox user’s guide. (1995)
[16] K. Gu, An integral inequality in the stability problem of time-delay systems. In: Proc. IEEE CDC, Australia, 2000, pp. 2805 -- 2810.
[17] Yue, D.; Won, S.: Delay-dependent robust stability of stochastic systems with time delay and nonlinear uncertainties. Elect. lett. 37, 992-993 (2001) · Zbl 1190.93095
[18] Hale, J.; Lunel, S. M. Verduyn: Introduction to functional differential equations. (1993) · Zbl 0787.34002