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Global exponential stability of uncertain fuzzy BAM neural networks with time-varying delays. (English) Zbl 1198.93192
Summary: The Takagi-Sugeno (TS) fuzzy model representation is extended to the stability analysis for uncertain Bidirectional Associative Memory (BAM) neural networks with time-varying delays using linear matrix inequality (LMI) theory. A novel LMI-based stability criterion is obtained by LMI optimization algorithms to guarantee the exponential stability of uncertain BAM neural networks with time-varying delays which are represented by TS fuzzy models. Finally, the proposed stability conditions are demonstrated with numerical examples.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

93D20 Asymptotic stability in control theory
93C42 Fuzzy control/observation systems
LMI toolbox
Full Text: DOI
[1] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE trans syst man cybern, 15, 116-132, (1985) · Zbl 0576.93021
[2] Cao, Y.Y.; Frank, P.M., Stability analysis and synthesis of nonlinear time-delay systems via linear takagi – sugeno fuzzy models, Fuzzy set syst, 124, 213-229, (2001) · Zbl 1002.93051
[3] Takagi, T.; Sugeno, M., Stability analysis and design of fuzzy control systems, Fuzzy set syst, 45, 135-156, (1993)
[4] Cao, S.G.; Rees, N.W.; Feng, G., Stability analysis and design for a class of continuous-time fuzzy control systems, Int J control, 64, 6, 1069-1087, (1996) · Zbl 0867.93053
[5] Tanaka, K.; Ikede, T.; Wang, H.O., Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, \(H^\infty\) control theory, and linear matrix inequalities, IEEE trans fuzzy syst, 4, 1-13, (1996)
[6] Mussot, M.D.C.; Dias, R.C., Fuzzy sets and physics, Rev MAX fis, 39, 2, 295-303, (1993) · Zbl 1291.03108
[7] Thiang; Wijaya, A.H., Remote fuzzy logic control for a DC motor speed control, J tek elek, 2, 1, 8-12, (2002)
[8] Cheok, A.D.; Ertugrul, N., High robustness and reliability of fuzzy logic based position estimation for sensorless switched reluctance motor drives, IEEE trans power electr, 15, 2, 319-334, (2000)
[9] Liu, Y.K.; Xia, H.; Xie, C.L., Application of fuzzy neural network to the nuclear power plant in process fault diagnosis, Expert syst appl, 32, 2, 358-363, (2007)
[10] Arik, S., Global asymptotic stability of bidirectional associative memory neural networks with time delays, IEEE trans neural netw, 16, 580-586, (2005)
[11] Cao, J.; Wang, L., Periodic oscillatory solution of bidirectional associative memory networks, Phys rev E, 61, 1825-1828, (2000)
[12] Gopalsamy, K.; He, X.Z., Delay independent stability in bidirectional associative memory networks, IEEE trans neural netw, 5, 998-1002, (1994)
[13] Huang, Z.; Xia, Y., Global exponential stability of BAM neural networks with transmission delays and nonlinear impulses, Chaos, solitons & fractals, 38, 489-498, (2008) · Zbl 1154.34381
[14] Kosko, B., Adaptive bidirectional associative memories, Appl opt, 26, 4947-4960, (1987)
[15] Lou, X.; Cui, B., Robust asymptotic stability of uncertain fuzzy BAM neural networks with time-varying delays, Fuzzy set syst, 158, 2746-2756, (2007) · Zbl 1133.93366
[16] Senan, S.; Arik, S., Global robust stability of bidirectional associative memory neural networks with multiple time delays, IEEE trans syst man cybern B, 37, 1375-1381, (2007)
[17] Zhao, H.; Ding, N., Dynamic analysis of stochastic bidirectional associative memory neural networks with delays, Chaos, solitons & fractals, 32, 1692-1702, (2007) · Zbl 1149.34054
[18] Zheng, B.; Zhang, Y.; Zhang, C., Global existence of periodic solutions on a simplified BAM neural network model with delays, Chaos, solitons & fractals, 37, 1397-1408, (2008) · Zbl 1142.34370
[19] Liu, X.; Dickson, R., Stability analysis of Hopfield neural networks with uncertainty, Math comput model, 34, 353-363, (2001) · Zbl 0999.34052
[20] Singh, V., New global stability results for delayed cellular neural networks based on norm-bounded uncertainties, Chaos, solitons & fractals, 30, 1165-1171, (2006) · Zbl 1142.34353
[21] Zhang, H.B.; Liao, X.F., LMI-based robust stability analysis of neural networks with time-varying delay, Neurocomputing, 67, 306-312, (2005)
[22] Cao, J.; Dong, M., Exponential stability of delayed bi-directional associative memory networks, Appl math comput, 135, 105-112, (2003) · Zbl 1030.34073
[23] Chen, A.; Cao, J.; Huang, L., Exponential stability of BAM neural networks with transmission delays, Neurocomputing, 57, 435-454, (2004)
[24] Huang, H.; Ho, D.W.C.; Lam, J., Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays, IEEE trans circ syst II exp briefs, 52, 251-255, (2005)
[25] Gahinet, P.; Nemirovski, A.; Laub, A.; Chilali, M., LMI control toolbox user’s guide, (1995), The Mathworks Massachusetts
[26] Boyd, B.; Ghoui, L.E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia
[27] Liao, X.F.; Chen, G.R.; Sanchez, E.N., Delay-dependent exponential stability of delayed neural networks: an LMI approach, Neural netw, 15, 855-866, (2002)
[28] Mao, X.; Koroleva, N.; Rodkina, A., Robust stability of uncertain stochastic delay differential equations, Syst control lett, 35, 325-336, (1998) · Zbl 0909.93054
[29] De Souza, C.E.; Li, X., Delay-dependent robust control of uncertain linear state-delayed systems, Automatica, 35, 1313-1321, (1999) · Zbl 1041.93515
[30] Cao, J.; Yuan, K.; Li, H.X., Global asymptotic stability of recurrent neural networks with multiple discrete delays and distributed delays, IEEE trans neural netw, 17, 1646-1651, (2006)
[31] Wang, Z.; Qiao, H., Robust filtering for bilinear uncertain stochastic discrete-time systems, IEEE trans signal process, 50, 560-567, (2002) · Zbl 1369.93661
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