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A novel criterion for global asymptotic stability of BAM neural networks with time delays. (English) Zbl 1121.92006
Summary: A delay-differential equation modelling a bidirectional associative memory (BAM) neural networks is investigated. An asymptotic stability of the BAM neural networks with time delays is considered by constructing a new suitable Lyapunov functional and some matrix inequality techniques. A novel delay-dependent stability criterion is given in terms of matrix inequalities, which can be solved easily by optimization algorithms.

MSC:
92B20General theory of neural networks (mathematical biology)
34K20Stability theory of functional-differential equations
34K60Qualitative investigation and simulation of models
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References:
[1] Kosko, B.: Adaptive bidirectional associative memories. Appl opt 26, 4947-4960 (1987)
[2] Kosko, B.: Bidirectional associative memories. IEEE trans syst man cyber 18, 49-60 (1988)
[3] Gopalsamy, K.; He, X. Z.: Delay-independent stability in bidirectional associative memory networks. IEEE trans neural networks 5, 998-1002 (1994)
[4] Cao, J.; Wang, L.: Periodic oscillatory solution of bidirectional associative memory networks. Phys rev E 61, 1825-1828 (2000)
[5] Guo, S. J.; Huang, L. H.; Dai, B. X.; Zhang, Z. Z.: Global existence of periodic solutions of BAM neural networks with variable coefficients. Phys lett A 317, 97-106 (2003) · Zbl 1046.68090
[6] Liao, X.; Yu, J.: Qualitative analysis of bidirectional associative memory with time delay. Int J circ theory appl 26, 219-229 (1998) · Zbl 0915.94012
[7] Zhang, J.; Yang, Y.: Global stability analysis of bidirectional associative memory neural networks with time delay. Int J circ theory appl 29, 185-196 (2001) · Zbl 1001.34066
[8] Zhao, H.: Global stability of bidirectional associative memory neural networks with distributed delays. Phys lett A 297, 182-190 (2002) · Zbl 0995.92002
[9] Cao, J.: Global asymptotic stability of delayed bi-directional associative memory neural networks. Appl math comput 142, 333-339 (2003) · Zbl 1031.34074
[10] Chen, A.; Huang, L.; Cao, J.: Existence and stability of almost periodic solution for BAM neural networks with delays. Appl math comput 137, 177-193 (2003) · Zbl 1034.34087
[11] Huang, X.; Cao, J.; Huang, D. S.: LMI-based approach for delay-dependent exponential stability analysis of BAM neural networks. Chaos, solitons & fractals 24, 885-898 (2005) · Zbl 1071.82538
[12] Boyd, B.; Ghaoui, L. E.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in systems and control theory. (1994) · Zbl 0816.93004
[13] Gahinet, P.; Nemirovski, A.; Laub, A.; Chilali, M.: LMI control toolbox user’s guide. (1995)
[14] Gu K. An integral inequality in the stability problem of time-delay systems. In: Proc IEEE CDC, Australia, December 2000. p. 2805-10.
[15] 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
[16] Hale, J.; Lunel, S. M. Verduyn: Introduction to functional differential equations. (1993) · Zbl 0787.34002
[17] Cao, Y. Y.; Sun, Y. X.; Lam, J.: Delay-dependent robust H$\infty $control for uncertain systems with time-varying delays. IEEE proc--control theory appl 145, 338-343 (1998)