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Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays. (English) Zbl 1111.68104
Summary: This paper discusses a generalized model of high-order Hopfield-type neural networks with time-varying delays. Some novel global stability criteria of the system is derived by using Lyapunov method, Linear Matrix Inequality (LMI) and analytic technique. The LMI-based criteria obtained here are computationally more flexible and more generic than many other existing criteria. A numerical example is given to illustrate our result.

MSC:
68T05Learning and adaptive systems
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References:
[1] Hopfield, J. J.: Neural networks and physical systems with emergent collective computational abilities. Proc. natl. Acad. sci. 79, 2554-2558 (1982)
[2] Hopfield, J. J.: Neurons with graded response have collective computational properties like those of two-state neurons. Proc. natl. Acad. sci. 81, 3088-3092 (1984)
[3] Gopalsamy, K.; He, X. Z.: Stability in asymmetric Hopfield nets with transmission delays. Phys. D 76, No. 4, 344-358 (1994) · Zbl 0815.92001
[4] Cao, J.: Global exponential stability of Hopfield neural networks. Internat. J. Systems sci. 32, 233-236 (2001) · Zbl 1011.93091
[5] Xu, Z. B.: Global convergence and asymptotic stability of asymmetric Hopfield neural networks. J. math. Anal. appl. 191, 405-427 (1995) · Zbl 0819.68101
[6] Zhang, Q.; Wei, X. P.; Xu, J.: Global asymptotic stability of Hopfield neural networks with transmission delays. Phys. lett. A 318, 399-405 (2003) · Zbl 1030.92003
[7] Zhang, J. Y.; Jin, X. S.: Global stability analysis in delayed Hopfield neural network models. Neural networks 13, 745-753 (2000)
[8] 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
[9] 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
[10] X.Y. Lou, B.T. Cui, Absolute exponential stability analysis of delayed bi-directional associative memory neural networks, Chaos Solitons Fractals, in press · Zbl 1147.34358
[11] X.Y. Lou, B.T. Cui, New LMI conditions for delay-dependent asymptotic stability of delayed Hopfield neural networks, Neurocomputing, in press
[12] Liao, X. X.: Stability of Hopfield-type neural networks (I). Sci. China ser. A 38, No. 4, 407-418 (1995) · Zbl 0837.68098
[13] Liao, X. X.; Liao, Y.: Stability of Hopfield-type neural networks (II). Sci. China ser. A 40, No. 8, 813-816 (1997) · Zbl 0886.68115
[14] Liao, X. X.; Xiao, D. M.: Global exponential stability of Hopfield neural networks with time-varying delays. Acta electron. Sinica 28, No. 4, 87-90 (2000)
[15] Xu, B. J.; Liu, X. Z.; Liao, X. X.: Global asymptotic stability of high-order Hopfield type neural networks with time delays. Comput. math. Appl. 45, 1729-1737 (2003) · Zbl 1045.37056
[16] Cao, J.; Liang, J.; Lam, J.: Exponential stability of high-order bidirectional associative memory neural networks with time delays. Phys. D 199, 425-436 (2004) · Zbl 1071.93048
[17] Liu, X. Z.; Teo, K. L.: Exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays. IEEE trans. Neural networks 16, No. 6, 1329-1339 (2005)
[18] Sanchez, E. N.; Perez, J. P.: Input-to-state stability (ISS) analysis for dynamic NN. IEEE trans. Circuits syst. I 46, 1395-1398 (1999) · Zbl 0956.68133
[19] Khalil, H. K.: Nonlinear systems. (1988) · Zbl 0667.73052
[20] Simpson, P. K.: Higher-ordered and intraconnected bidirectional associative memories. IEEE trans. Syst. man cybernet. 20, 637-653 (1990)
[21] Ho, D. W. C.; Lam, J.; Xu, J.; Tam, H. K.: Neural computation for robust approximate pole assignment. Neurocomputing 25, 191-211 (1999) · Zbl 0941.68111
[22] Arik, S.: Global asymptotic stability of a larger class of neural networks with constant time delay. Phys. lett. A 311, 504-511 (2003) · Zbl 1098.92501
[23] Arik, S.; Tavsanoglu, V.: On the global asymptotic stability of delayed cellular neural networks. IEEE trans. Circuits syst. I 47, No. 4, 571-574 (2000) · Zbl 0997.90095
[24] Cao, J.: Global stability conditions for delayed cnns. IEEE trans. Circuits syst. I 48, No. 11, 1330-1333 (2001) · Zbl 1006.34070
[25] Arik, S.: An analysis of global asymptotic stability of delayed cellular neural networks. IEEE trans. Neural networks 13, No. 5, 1239-1242 (2002)
[26] Liao, X.; Chen, G. R.; Sanchenz, E. N.: Delay dependent exponential stability analysis of delayed neural networks: an LMI approach. Neural networks 15, 855-866 (2002)
[27] Ren, F.; Cao, J.: LMI-based criteria for stability of high-order neural networks with time-varying delay. Nonlinear anal. Ser. B 7, No. 5, 967-979 (2006) · Zbl 1121.34078
[28] Cao, J.; Li, X.: Stability in delayed Cohen -- Grossberg neural networks: LMI optimization approach. Phys. D 212, No. 1 -- 2, 54-65 (2005) · Zbl 1097.34053
[29] Cao, J.; Wang, J.: Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE trans. Circuits syst. I 52, No. 2, 417-426 (2005)
[30] Cao, J.; Song, Q.: Stability in Cohen -- Grossberg type BAM neural networks with time-varying delays. Nonlinearity 19, No. 7, 1601-1617 (2006) · Zbl 1118.37038