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An analysis of global robust stability of uncertain cellular neural networks with discrete and distributed delays. (English) Zbl 1144.93023
Summary: This paper considers the robust stability analysis of cellular neural networks with discrete and distributed delays. Based on the Lyapunov stability theory and linear matrix inequality (LMI) technique, a novel stability criterion guaranteeing the global robust convergence of the equilibrium point is derived. The criterion can be solved easily by various convex optimization algorithms. An example is given to illustrate the usefulness of our results.

MSC:
93D09Robust stability of control systems
92B20General theory of neural networks (mathematical biology)
34D23Global stability of ODE
93C15Control systems governed by ODE
93D09Robust stability of control systems
90C25Convex programming
Software:
LMI toolbox
WorldCat.org
Full Text: DOI
References:
[1] Chua, L.; Yang, L.: Cellular neural networks: theory and applications. IEEE trans circuits syst I 35, 1257-1290 (1988) · Zbl 0663.94022
[2] Liu, Y.; You, Z.; Cao, L.: Dynamical behaviors of Hopfield neural network with multilevel activation functions. Chaos, solitons & fractals 22, 1141-1153 (2005) · Zbl 1067.92005
[3] Chen, C. J.; Liao, T. L.; Hwang, C. C.: Exponential synchronization of a class of chaotic neural networks. Chaos, solitons & fractals 24, 197-206 (2005) · Zbl 1060.93519
[4] Yang, X.; Liao, X.; Bai, S.; Evans, D. J.: Robust exponential stability and domains of attraction in a class of interval neural networks. Chaos, solitions & fractals 26, 445-451 (2005) · Zbl 1112.34326
[5] Cheng, C. J.; Liao, T. L.; Hwang, C. C.: Exponential synchronization of a class of chaotic neural networks. Chaos, solitions & fractals 24, 197-206 (2005) · Zbl 1060.93519
[6] Tu, F.; Liao, X.: Harmless delays for global asymptotic stability of Cohen-Grossberg neural networks. Chaos, solitons & fractals 26, 927-933 (2005) · Zbl 1088.34064
[7] Cao, J.; Ho, D. W. C.: A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach. Chaos, solitons & fractals 24, 1317-1329 (2005) · Zbl 1072.92004
[8] Zhou, S.; Liao, X.; Wu, Z.; Wong, K.: Hopf bifurcation in a control system for the washout filter-based delayed neural equation. Chaos, solitons & fractals 23, 101-115 (2005) · Zbl 1071.93042
[9] Cao, J.: Global asymptotic stability of neural networks with transmission delays. Int J syst sci 31, 1313-1316 (2000) · Zbl 1080.93517
[10] Chen, A.; Cao, J.; Huang, L.: An estimation of upperbound of delays for global asymptotic stability of delayed Hopfield neural networks. IEEE trans circuits syst I 49, 1028-1032 (2002)
[11] Liao, T. L.; Wang, F. C.: Global stability for cellular neural networks with time delay. IEEE trans neural network 11, 1481-1484 (2000)
[12] Cao, J.: Global stability conditions for delayed cnns. IEEE trans circuits syst I 48, 1330-1333 (2001) · Zbl 1006.34070
[13] Arik, S.: An analysis of global asymptotic stability of delayed cellular neural networks. IEEE trans neural network 13, 1239-1242 (2002)
[14] Singh, V.: Robust stability of cellular neural networks with delay: linear matrix inequality approach. IEE proc control theory appl 151, 125-129 (2004)
[15] Ruan, S.; Filfil, R. S.: Dynamics of a two-neuron system with discrete and distributed delays. Physica D 191, 323-342 (2004) · Zbl 1049.92004
[16] Liang, J.; Cao, J.: Global asymptotic stability of bi-directional associative memory networks with distributed delays. Appl math comput 152, 415-424 (2004) · Zbl 1046.94020
[17] Zhao, H.: Global stability of bidirectional associative memory neural networks with distributed delays. Phys lett A 297, 182-190 (2002) · Zbl 0995.92002
[18] Wang, Z.; Liu, Y.; Liu, X.: On global asymptotic stability of neural networks with discrete and distributed delays. Phys lett A 345, 299-308 (2005) · Zbl 05314210
[19] Boyd, B.; Ghaoui, L. E.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in systems and control theory. (1994) · Zbl 0816.93004
[20] Gahinet, P.; Nemirovski, A.; Laub, A.; Chilali, M.: LMI control toolbox user’s guide. (1995)
[21] Gu K. An integral inequality in the stability problem of time-delay systems. In: Proc IEEE CDC. Australia, December 2000. p. 2805-10.
[22] Yue, D.; Won, S.: Delay-dependent robust stability of stochastic systems with time delay and nonlinear uncertainties. Electron lett 37, 992-993 (2001) · Zbl 1190.93095
[23] Hale, J.; Lunel, S. M. Verduyn: Introduction to functional differential equations. (1993) · Zbl 0787.34002