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.


92B20 Neural networks for/in biological studies, artificial life and related topics
34K20 Stability theory of functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations


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[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), SIAM Philadelphia
[13] Gahinet, P.; Nemirovski, A.; Laub, A.; Chilali, M., LMI control toolbox user’s guide, (1995), The Mathworks Massachusetts
[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.; Verduyn Lunel, S.M., Introduction to functional differential equations, (1993), Springer-Verlag New York · Zbl 0787.34002
[17] Cao, Y.Y.; Sun, Y.X.; Lam, J., Delay-dependent robust H∞ control for uncertain systems with time-varying delays, IEEE proc—control theory appl, 145, 338-343, (1998)
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