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Global robust dissipativity for integro-differential systems modeling neural networks with delays. (English) Zbl 1141.93392
Summary: The global robust dissipativity of integro-differential systems modeling neural networks with time-varying delays are studied. Proper Lyapunov functionals and some analytic techniques are employed to derive the sufficient conditions under which the networks proposed are the global robust dissipativity. The results are shown to improve the previous global dissipativity results derived in the literature. Some examples are given to illustrate the correctness of our results.

93D05Lyapunov and other classical stabilities of control systems
93C30Control systems governed by other functional relations
92B20General theory of neural networks (mathematical biology)
Full Text: DOI
[1] Arik, S.: Global robust stability of delayed neural networks, IEEE trans circ syst I 50, No. 1, 156-160 (2003)
[2] Cao, J.; Huang, D.; Qu, Y.: Global robust stability of delayed recurrent neural networks, Chaos, solitons & fractals 23, 221-229 (2005) · Zbl 1075.68070 · doi:10.1016/j.chaos.2004.04.002
[3] 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
[4] Cao, J.; Dong, M.: Exponential stability of delayed bi-directional associative memory networks, Appl math comput 135, 105-112 (2003) · Zbl 1030.34073 · doi:10.1016/S0096-3003(01)00315-0
[5] Chen, A.; Cao, J.; Huang, L.: Exponential stability of BAM neural networks with transmission delays, Neurocomputing 57, 435-454 (2004)
[6] Li, Y.: Global exponential stability of BAM neural networks with delays and impulses, Chaos, solitons & fractals 24, 279-285 (2005) · Zbl 1099.68085
[7] Cao, J.: On exponential stability and periodic solutions of cnns with delays, Phys lett A 267, No. 5-6, 312-318 (2000) · Zbl 1098.82615 · doi:10.1016/S0375-9601(00)00136-5
[8] Cao, J.; Liang, J.: Boundedness and stability for Cohen -- Grossberg neural network with time-varying delays, J math anal appl 296, 665-685 (2004) · Zbl 1044.92001 · doi:10.1016/j.jmaa.2004.04.039
[9] Zhang, Q.; Wei, X.; Xu, J.: Delay-dependent exponential stability of cellular neural networks with time-varying delays, Chaos, solitons & fractals 23, 1363-1369 (2005) · Zbl 1094.34055
[10] Cui, B. T.; Lou, X. Y.: Global asymptotic stability of BAM neural networks with distributed delays and reaction -- diffusion terms, Chaos, solitons & fractals 27, No. 5, 1347-1354 (2006) · Zbl 1084.68095
[11] Lou, X. Y.; Cui, B. T.: Global asymptotic stability of delay BAM neural networks with impulses, Chaos, solitons & fractals 29, No. 4, 1023-1031 (2006) · Zbl 1142.34376
[12] Lou XY, Cui BT. A new LMI condition for delay-dependent asymptotic stability of delayed cellular neural networks. Neurocomputing, in press.
[13] Lou XY, Cui BT. Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters. J Math Anal Appl, in press. · Zbl 1132.34061 · doi:10.1016/j.jmaa.2006.05.041
[14] Liu, Z.; Liao, L.: Existence and global exponential stability of periodic solution of cellular neural networks with time-varying delays, J math anal appl 290, 247-262 (2004) · Zbl 1055.34135 · doi:10.1016/j.jmaa.2003.09.052
[15] Jiang, H.; Teng, Z.: Global exponential stability of cellular neural networks with time-varying coefficients and delays, Neural networks 17, 1415-1425 (2004) · Zbl 1068.68121 · doi:10.1016/j.neunet.2004.03.002
[16] Liao, X.; Wang, J.: Global dissipativity of continuous-time recurrent neural networks with time delay, Phys rev E 68, 1-7 (2003)
[17] Arik, S.: On the global dissipativity of dynamical neural networks with time delays, Phys lett A 326, 126-132 (2004) · Zbl 1161.37362 · doi:10.1016/j.physleta.2004.04.023
[18] Song, Q.; Zhao, Z.: Global dissipativity of neural networks with both variable and unbounded delays, Chaos, solitons & fractals 25, 393-401 (2005) · Zbl 1072.92005
[19] Hale, J. K.; Lunel, S. M. V.: Introduction to the theory of functional differential equations, Applied mathematical sciences (1991) · Zbl 0751.34037