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Delay-range-dependent exponential \(H\infty \) synchronization of a class of delayed neural networks. (English) Zbl 1198.93179
Summary: This article aims to present a multiple delayed state-feedback control design for exponential \(H\infty \) synchronization problem of a class of delayed neural networks with multiple time-varying discrete delays. On the basis of the drive-response concept and by introducing a descriptor technique and using Lyapunov-Krasovskii functional, new delay-range-dependent sufficient conditions for exponential \(H\infty \) synchronization of the drive-response structure of neural networks are driven in terms of linear matrix inequalities (LMIs). The explicit expression of the controller gain matrices are parameterized based on the solvability conditions such that the drive system and the response system can be exponentially synchronized. A numerical example is included to illustrate the applicability of the proposed design method.
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.

MSC:
93D15 Stabilization of systems by feedback
93B36 \(H^\infty\)-control
37N35 Dynamical systems in control
92B20 Neural networks for/in biological studies, artificial life and related topics
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[1] Pecora, L.M.; Carrol, T.L., Synchronization in chaotic systems, Phys rev lett, 64, 821-823, (1990)
[2] Zhang, H.; Wang, Z.; Liu, D., Robust exponential stability of recurrent neural networks with multiple time-varying delays, IEEE trans circ syst II: express briefs, 54, 8, 730-734, (2007)
[3] Wang, Z.; Liu, Y.; Yu, L.; Liu, X., Exponential stability of delayed recurrent neural networks with Markovian jumping parameters, Phys lett A, 356, 346-352, (2006) · Zbl 1160.37439
[4] Mou, S.S.; Gao, H.J.; Qiang, W.Y.; Chen, K., New delay-dependent exponential stability for neural networks with time delay, IEEE trans syst man cybernet part B - cybernet, 38, 2, 571-576, (2008)
[5] Xu, S.; Lam, J.; Ho, D.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
[6] Mou, S.S.; Gao, H.J.; Lam, J.; Qiang, W.Y., A new criterion of delay-dependent asymptotic stability for Hopfield neural networks with time delay, IEEE trans neural networks, 19, 3, 532-535, (2008)
[7] Xu, S.; Lam, J.; Ho, D.W.C.; Zou, Y., Global robust exponential stability analysis for interval recurrent neural networks, Phys lett A, 325, 124-133, (2004) · Zbl 1161.93335
[8] Cheng, C.J.; Liao, T.L.; Yan, J.J.; Hwang, C.C., Exponential synchronization of a class of neural networks with time-varying delays, IEEE trans syst man cybernet part B: cybernet, 36, 1, 209-215, (2006)
[9] Lu, H.; van Leeuwen, C., Synchronization of chaotic neural networks via output or state coupling, Chaos, solitons & fractals, 30, 166-176, (2006) · Zbl 1144.37377
[10] Hou, Y.Y.; Liao, T.L.; Yan, J.J., \(H_\infty\) synchronization of chaotic systems using output feedback control design, Physics A, 379, 81-89, (2007)
[11] Lu, J.; Cao, J., Synchronization-based approach for parameters identification in delayed chaotic neural networks, Physics A, 382, 672-682, (2007)
[12] Gao, H.J.; Lam, J.; Chen, G.R., New criteria for synchronization stability of general complex dynamical networks with coupling delays, Phys lett A, 360, 2, 263-273, (2006) · Zbl 1236.34069
[13] Sun, Y.; Cao, J.; Wang, Z., Exponential synchronization of stochastic perturbed chaotic delayed neural networks, Neurocomputing, 70, 2477-2485, (2007)
[14] Yu, W.; Cao, J., Synchronization control of stochastic delayed neural networks, Physics A, 373, 252-260, (2007)
[15] Cheng, C.J.; Liao, T.L.; Yan, J.J.; Hwang, C.C., Synchronization of neural networks by decentralized feedback control, Phys lett A, 338, 28-35, (2005) · Zbl 1136.37366
[16] Li, P.; Cao, J.; Wang, Z., Robust impulsive synchronization of coupled delayed neural networks with uncertainties, Physics A, 373, 261-272, (2007)
[17] Liao, T.L.; Tsai, S.H., Adaptive synchronization of chaotic systems and its application to secure communication, Chaos, solitons & fractals, 11, 9, 1387-1396, (2000) · Zbl 0967.93059
[18] Feki, M., An adaptive chaos synchronization scheme applied to secure communication, Chaos, solitons & fractals, 18, 141-148, (2003) · Zbl 1048.93508
[19] Sun, Y.; Cao, J., Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation, Phys lett A, 364, 277-285, (2007) · Zbl 1203.93110
[20] Zhou, J.; Chen, T.; Xiang, L., Robust synchronization of delayed neural networks based on adaptive control and parameters identification, Chaos, solitons & fractals, 27, 905-913, (2006) · Zbl 1091.93032
[21] Yu W, Cao J. Adaptive Q-S (lag, anticipated, and complete) time-varying synchronization and parameters identification of uncertain delayed neural networks. In: Chaos, vol. 16, Article no. 023119; 2006. · Zbl 1146.93371
[22] Chen, M.; Zhou, D.; Shang, Y., A new observer-based synchronization scheme for private communication, Chaos, solitons & fractals, 24, 1025-1030, (2005) · Zbl 1069.94508
[23] Cao, J.; Li, P.; Wang, W., Global synchronization in arrays of delayed neural networks with constant or delayed coupling, Phys lett A, 353, 318-325, (2006)
[24] Cai, G.P.; Huang, J.Z.; Yang, S.X., An optimal control method for linear systems with time delay, Comput struct, 81, 1539-1546, (2003) · Zbl 1038.33009
[25] Niculescu, S.I., Delay effects on stability: a robust control approach, (2001), Springer Berlin
[26] Krasovskii, N.N., Stability of motion, (1963), Stanford University Press Stanford, CA · Zbl 0109.06001
[27] Gu K. An integral inequality in the stability problem of time-delay systems. In: Proceedings of the 39th IEEE conference on decision and control; 2000. p. 2805-10.
[28] Cao, J., Periodic oscillation and exponentially stability of delayed cnns, Phys lett A, 270, 157-163, (2000)
[29] Chen, A.; Cao, J.; Huang, L., Global robust stability of interval cellular neural networks with time-varying delays, Chaos, solitons & fractals, 23, 787-799, (2005) · Zbl 1101.68752
[30] Khalil, H.K., Nonlinear systems, (1992), Macmillan New York · Zbl 0626.34052
[31] Fridman, E.; Shaked, U., A descriptor system approach to \(H_\infty\) control of linear time-delay systems, IEEE trans automat control, 47, 2, 253-270, (2002) · Zbl 1364.93209
[32] Gao, H.; Wang, C., Comments and further results on A descriptor system approach to \(H_\infty\) control of linear time-delay systems, IEEE trans automat control, 48, 520-525, (2003) · Zbl 1364.93211
[33] 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
[34] He, Y.; Wang, Q.G.; Lin, C.; Wu, M., Delay-range-dependent stability for systems with time-varying delay, Automatica, 43, 371-376, (2007) · Zbl 1111.93073
[35] Moon, Y.S.; Park, P.G.; 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
[36] Gao, H.J.; Lam, J.; Wang, Z.D., Discrete bilinear stochastic systems with time-varying delay: stability analysis and control synthesis, Chaos, solitons & fractals, 34, 2, 394-404, (2007) · Zbl 1134.93413
[37] Karimi, H.R., Observer-based mixed \(H_2 / H_\infty\) control design for linear systems with time-varying delays: an LMI approach, Int J control automat syst, 6, 1, 1-14, (2008)
[38] Lee, Y.S.; Moon, Y.S.; Kwon, W.H.; Park, P.G., Delay-dependent robust \(H_\infty\) control for uncertain systems with a state-delay, Automatica, 40, 65-72, (2004) · Zbl 1046.93015
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