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Robust exponential stability of Markovian jumping neural networks with mode-dependent delay. (English) Zbl 1222.93231
Summary: This paper deals with the robust exponential stability problem for a class of Markovian jumping neural networks with time delay. The delay considered varies randomly, depending on the mode of the networks. By using a new Lyapunov–Krasovskii functional, a delay-dependent stability criterion is presented, which can be expressed in terms of linear matrix inequalities (LMIs). A numerical example is given to show the effectiveness of the results.
MSC:
93E15Stochastic stability
34F05ODE with randomness
34K20Stability theory of functional-differential equations
92B20General theory of neural networks (mathematical biology)
References:
[1]Cao, J. D.; Yuan, K.; Li, H. X.: Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays, IEEE trans neural networks 17, 1646-1651 (2006)
[2]He, Y.; Wu, M.; She, J. H.: An improved global asymptotic stability criterion for delayed cellular neural networks, IEEE trans neural networks 17, 250-252 (2006)
[3]Xu, S. Y.; Lam, J.; Daniel, W. C.; Zou, Y.: Delay-dependent exponential stability for a class of neural networks with time delays, J comput appl math 183, 16-28 (2005) · Zbl 1097.34057 · doi:10.1016/j.cam.2004.12.025
[4]He, Y.; Liu, G. P.; Rees, D.: New delay-dependent stability criteria for neural networks with time-varying delay, IEEE trans neural networks 18, 310-314 (2007)
[5]Park, J. H.; Park, C. H.; Kwon, O. M.; Lee, S. M.: A new stability criterion for bidirectional associative memory neural networks of neutral-type, Appl math comput 199, 716-722 (2008) · Zbl 1149.34345 · doi:10.1016/j.amc.2007.10.032
[6]Park, J. H.; Kwon, O. M.: On improved delay-dependent criterion for global stability of bidirectional associative memory neural networks with time-varying delays, Appl math comput 199, 435-436 (2008) · Zbl 1149.34049 · doi:10.1016/j.amc.2007.10.001
[7]Liang, J. L.; Cao, J. D.: A based-on LMI stability criterion for delayed recurrent neural networks, Chaos solitons fract 28, 154-160 (2006) · Zbl 1085.68129 · doi:10.1016/j.chaos.2005.04.120
[8]Lou, X. Y.; Cui, B. T.: New LMI conditions for delay-dependent asymptotic stability of delayed Hopfield neural networks, Neurocomputing 69, 2374-2378 (2006)
[9]Nilsson, J.; Bernhardsson, B.; Wittenmark, B.: Stochastic analysis and control of real-time systems with random time delays, Automatica 34, 57-64 (1998) · Zbl 0908.93073 · doi:10.1016/S0005-1098(97)00170-2
[10]J. Nilsson, Real time control systems with delays, Department of Automatic Control, Lund Institute of Technology, Lund, Sweden; 1998.
[11]Rakkiyappan, R.; Balasubramaniam, P.: Delay-dependent asymptotic stability for stochastic delayed recurrent neural networks with time varying delays, Appl math comput 198, 526-533 (2008) · Zbl 1144.34375 · doi:10.1016/j.amc.2007.08.053
[12]Zhao, H. Y.; Ding, N.: Dynamic analysis of stochastic bidirectional associative memory neural networks with delays, Chaos solitons fract 32, 1692-1702 (2007) · Zbl 1149.34054 · doi:10.1016/j.chaos.2005.12.010
[13]Wang, Z. D.; Liu, Y. R.; Yu, L.; Liu, Xiaohui: Exponential stability of delayed recurrent neural networks with Markovian jumping parameters, Phys lett A 356, 346-352 (2006) · Zbl 1160.37439 · doi:10.1016/j.physleta.2006.03.078
[14]Lou, X. Y.; Cui, B. T.: Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters, J math anal appl 328, 316-326 (2007) · Zbl 1132.34061 · doi:10.1016/j.jmaa.2006.05.041
[15]Blythe, S.; Mao, X.; Liao, X.: Stability of stochastic delay neural networks, J franklin inst 338, 481-495 (2001) · Zbl 0991.93120 · doi:10.1016/S0016-0032(01)00016-3
[16]Wang, L. S.; Zhang, Z.; Wang, Y. F.: Stochastic exponential stability of the delayed reaction-diffusion recurrent neural networks with Markovian jumping parameters, Phys lett A 372, 3201-3209 (2008) · Zbl 1220.35090 · doi:10.1016/j.physleta.2007.07.090
[17]Wang, L. S.; Gao, Y. Y.: Global exponential robust stability of reaction-diffusion interval neural networks with time-varying delays, Phys lett A 350, 342-348 (2006) · Zbl 1195.35179 · doi:10.1016/j.physleta.2005.10.031
[18]Wang, Z. D.; Shu, H. S.; Fang, J. A.; Liu, X. H.: Robust stability for stochastic Hopfield neural networks with time delays, Nonlinear anal: real world appl 7, 1119-1128 (2006) · Zbl 1122.34065 · doi:10.1016/j.nonrwa.2005.10.004
[19]Wang, Z. D.; Fang, J. A.; Liu, X. H.: Global stability of stochastic high-order neural networks with discrete and distributed delays, Chaos solitons fract 36, 388-396 (2008) · Zbl 1141.93416 · doi:10.1016/j.chaos.2006.06.063
[20]Arik, S.: Global robust stability analysis of neural networks with discrete time delays, Chaos solitons fract 26, 1407-1414 (2005) · Zbl 1122.93397 · doi:10.1016/j.chaos.2005.03.025
[21]Singh, V.: Novel LMI condition for global robust stability of delayed neural networks, Chaos solitons fract 34, 503-508 (2007) · Zbl 1134.93393 · doi:10.1016/j.chaos.2006.03.034
[22]Boyd, S.; Ghaoui, L. E. I.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in system and control theory, (1994)
[23]Den Driessche, P. Van; Zou, X.: Global attractivity in delayed Hopfield neural network models, SIAM J appl math 58, 1878-1890 (1998) · Zbl 0917.34036 · doi:10.1137/S0036139997321219
[24]Sanchez, E. N.; Perez, J. P.: Input-to-state stability (ISS) analysis for dynamic NN, IEEE trans, circ syst I 46, 1395-1398 (1999) · Zbl 0956.68133 · doi:10.1109/81.802844