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Delay-dependent asymptotic stability for stochastic delayed recurrent neural networks with time varying delays. (English) Zbl 1144.34375

Summary: The global asymptotic stability of stochastic recurrent neural networks with time varying delays is analyzed. By utilizing a Lyapunov functional and combining it with the linear matrix inequality (LMI) approach, we analyze the global asymptotic stability of stochastic delayed recurrent neural networks. In addition, an example is provided to illustrate the applicability of the result.

MSC:

34K20 Stability theory of functional-differential equations
34K50 Stochastic functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
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[1] Cao, J.; Wang, J., Global asymptotic stability of a general class of recurrent neural networks with time-varying delays, IEEE trans. circuits. syst. I, 50, 34-44, (2003) · Zbl 1368.34084
[2] Chen, W.; Guan, Z.; Liu, X., Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach, Syst. control lett., 54, 547-555, (2005) · Zbl 1129.93547
[3] Chen, W.; Guan, Z.; Yu, P., Delay-dependent stability and \(H_\infty\) control of uncertain discrete-time Markovian jump systems with with mode-dependent time-delays, Syst. control lett., 52, 361-376, (2004) · Zbl 1157.93438
[4] Chen, W.; Xu, J.; Guan, Z., Guaranteed cost control for uncertain Markovian jump systems with mode-dependent time-delays, IEEE trans. automat. control, 48, 2270-2276, (2003) · Zbl 1364.93369
[5] Chua, L.O.; Yang, L., Cellular neural networks: theory and applications, IEEE trans. circuit. syst. I, 35, 1257-1290, (1988) · Zbl 0663.94022
[6] Elman, J.L., Finding structure in time, Cognitive sci., 14, 179-211, (1990)
[7] Fridman, E., New Lyapunov-krasovskii functionals for stability of linear retard and neutral type systems, Syst. control lett., 43, 309-319, (2001) · Zbl 0974.93028
[8] Fridman, E.; Shaked, U., A descriptor system approach to \(H_\infty\) control time delay systems, IEEE trans. automat. control, 47, 253-279, (2002) · Zbl 1364.93209
[9] Huang, H.; Ho, D.W.C.; Lam, J., Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays, IEEE trans. circuit. sys. II, 52, 251-255, (2005)
[10] Kolmanovskii, V.B.; Myskis, A.D., Introduction to the theory and applications of functional differential equations, (1999), Kluwer, Academic Publishers. Dordrecht
[11] Liao, X.; Mao, X., Exponential stability of stochastic delay interval systems, Syst. control lett., 40, 171-181, (2000) · Zbl 0949.60068
[12] Li, X.; de Souza, C.E., Delay dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach, IEEE trans. automat. control, 42, 1144-1148, (1997) · Zbl 0889.93050
[13] Mao, X., Robustness of exponential stability of stochastic differential delay equations, IEEE trans. automat. control, 41, 442-447, (1996) · Zbl 0851.93074
[14] Moon, Y.S.; Park, P.; Kwon, W.H.; Lee, Y.S., Delay-dependent robust stabilization of uncertain state-delayed systems, Int. J. control, 74, 1447-1455, (2001) · Zbl 1023.93055
[15] Marcus, C.M.; Westervelt, R.M., Stability of analog neural networks with delays, Phys. rev. A, 39, 347-359, (1989)
[16] Niculescu, S.L., On delay-dependent stability under model transformation of some neutral linear systems, Int. J. control, 74, 609-617, (2001) · Zbl 1047.34088
[17] A.P. Paplinski, Lecture Notes on Feedforward Multilayer Neural Networks, NNet(L.5) 2004.
[18] Park, P., A delay-dependent stability criterion for systems with uncertain time-invariant delays, IEEE trans. automat. control, 44, 876-877, (1999) · Zbl 0957.34069
[19] Park, J.H., A new delay dependent criterion for neutral systems with multiple delays, J. comput. appl. math, 136, 177-184, (2001) · Zbl 0995.34069
[20] Roska, T.; Wu, C.W.; Balsi, M.; Chua, L.O., Stability and dynamics of delay-type cellular neural networks, IEEE trans. circuits. syst., 39, 487-490, (1990) · Zbl 0775.92010
[21] Q. Song, Z. Wang, Neural networks with discrete and distributed time-varying delays: A general stability analysis, Chaos Soliton. Fract., in press. · Zbl 1142.34380
[22] Yue, D.; Han, Q., Delay-dependent exponential stability of stochastic systems with time varying delay, nonlinearity, and Markovian switching, IEEE trans. automat. control, 50, 217-222, (2005) · Zbl 1365.93377
[23] Yue, D.; Won, S., Delay-dependent robust stability of stochastic systems with time delay and nonlinear uncertainties, IEE electron. lett., 37, 992-993, (2001) · Zbl 1190.93095
[24] Zhang, Q.; Wei, X.; Xu, J., Delay-dependent exponential stability of cellular neural networks with time-varying delays, Chaos soliton. fract., 23, 1363-1369, (2005) · Zbl 1094.34055
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