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Finite-time synchronization control of complex dynamical networks with time delay. (English) Zbl 1311.34157

Summary: The finite-time synchronization between two complex networks with non-delayed and delayed coupling is proposed by using the impulsive control and the periodically intermittent control. Some novel and useful finite-time synchronization criteria are derived based on finite-time stability theory. Especially, the traditional synchronization criteria are improved by using the impulsive control and the periodically intermittent control in the convergence time, the results of this paper are important. Finally, numerical examples are given to verify the effectiveness and correctness of the synchronization criteria.

MSC:

34K25 Asymptotic theory of functional-differential equations
34D20 Stability of solutions to ordinary differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
34K35 Control problems for functional-differential equations
34K45 Functional-differential equations with impulses
34K20 Stability theory of functional-differential equations
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[1] Wang, X. F.; Chen, G. R., Synchronization in scale-free dynamical networks: robustness and fragility, IEEE Trans Circ Syst I, 49, 54-62 (2002) · Zbl 1368.93576
[2] Liao, X. F.; Chen, G. R.; Sanchezc Edgar, N., Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach, Neural Networks, 15, 855-866 (2002)
[3] Zhou, J.; Lu, J. A.; Lü, J. H., Adaptive synchronization of an uncertain complex dynamical network, IEEE Trans Autom Control, 51, 652-656 (2006) · Zbl 1366.93544
[4] Zhou, J.; Lu, J. A.; Lü, J. H., Pinning adaptive synchronization of a general complex dynamical network, Automatica, 44, 996-1003 (2008) · Zbl 1283.93032
[5] Vincent, U. E.; Guo, R. W., Finite-time synchronization for a class of chaotic and hyperchaotic systems via adaptive feedback controller, Phys Lett A, 375, 2322-2326 (2011) · Zbl 1242.34078
[6] Park, J. H., Synchronization of cellular neural networks of neural type via dynamic feedback controller, Chaos Solitons Fract, 42, 1299-1304 (2009) · Zbl 1198.93182
[7] Shen, Y. J.; Huang, Y. H.; Gu, Jason, Global finite-time observers for lipschitz nonlinear systems, IEEE Trans Autom Control, 56, 418-424 (2011) · Zbl 1368.93057
[8] Shen, Y. J.; Huang, Y. H., Uniformly observable and globally lipschitzian nonlinear system admit global finite-time observers, IEEE Trans Autom Control, 54, 2621-2625 (2009) · Zbl 1367.93097
[9] Yang, X. S.; Cao, J. D.; Lu, J. Q., Synchronization of delayed complex dynamical networks with impulsive and stochastic effects, Nonlinear Anal RWA, 12, 2252-2266 (2011) · Zbl 1223.37115
[10] Zhang, Q. J.; Lu, J. A.; Zhao, J. C., Impulsive synchronization of general continuous and discrete-time complex dynamical networks, Commun Nonlinear Sci Numer Simul, 15, 1063-1070 (2010) · Zbl 1221.93107
[11] Sun, M.; Zeng, C. Y.; Tao, Y. W.; Tian, L. X., Adaptive-impulsive synchronization in drive-response networks of continuous systems and its application, Phys Lett A, 373, 3041-3046 (2009) · Zbl 1233.34019
[12] Zheng, S.; Dong, G. G.; Bi, Q. S., Impulsive synchronization of complex networks with non-delayed and delayed coupling, Phys Lett A, 373, 4255-4259 (2009) · Zbl 1234.05220
[13] Cai, S. M.; Zhou, J.; Xiang, L.; Liu, Z. R., Robust impulsive synchronization of complex delayed networks, Phys Lett A, 372, 4990-4995 (2008) · Zbl 1221.34075
[14] Xia, W. G.; Cao, J. D., Pinning synchronization of delayed dynamical networks via periodically intermittent control, Chaos, 19, 013120 (2009) · Zbl 1311.93061
[15] Cai, S. M.; Liu, Z. R.; Xu, F. D.; Shen, J. W., Periodically intermittent controlling complex dynamcial networks with time-varying delays to a desired orbit, Phys Lett A, 373, 3846-3854 (2009) · Zbl 1234.34035
[16] Cai, S. M.; Hao, J. J.; He, Q. B.; Liu, Z. R., Exponential synchronization of complex delayed dynamical networks via pinning periodically intermittent control, Phys Lett A, 375, 1965-1971 (2011) · Zbl 1242.05253
[17] Wang, Y. J.; Hao, J. N.; Zuo, Z. Q., A new method for exponential synchronization of chaotic delayed systems via intermittent control, Phys Lett A, 374, 2024-2029 (2010) · Zbl 1236.34073
[18] Yu, J.; Hu, C.; Jiang, H. J.; Teng, Z. D., Synchronization of nonlinear systems with delays via periodically nonlinear intermittent control, Commun Nonlinear Sci Numer Simul, 17, 2978-2989 (2012) · Zbl 1243.93040
[19] Zhu, H. B.; Cui, B. T., Stabilization and synchronization of chaotic systems via intermittent control, Commun Nonlinear Sci Numer Simul, 15, 3577-3586 (2010) · Zbl 1222.93194
[20] Yang, T., Impulsive control theory (2001), Springer-verlag: Springer-verlag Berlin
[21] Li, C. D.; Feng, G.; Liao, X. F., Stabilization of nonlinear systems via periodically intermittent control, IEEE Trans Circ Syst II, 54, 1019-1023 (2007)
[22] Cai, S. M.; He, Q. B.; Hao, J. J.; Liu, Z. R., Exponential synchronization of complex networks with nonidentical time-delayed dynamical nodes, Phys Lett A, 374, 2539-2550 (2010) · Zbl 1236.05185
[23] Hu, C.; Yu, J.; Jiang, H. J.; Teng, Z. D., Exponential synchronization of complex networks with finite distributed delays coupling, IEEE Trans Neural Networks, 22, 1999-2010 (2007)
[24] Yang, X. S.; Cao, J. D., Finite-time stochastic synchronization of complex networks, Appl Math Modell, 34, 3631-3641 (2010) · Zbl 1201.37118
[25] Huang, X. Q.; Lin, W.; Yang, B., Global finite-time synchronization of a class of uncertain nonlinear systems, Automatica, 41, 881-888 (2005) · Zbl 1098.93032
[26] Wang, H.; Han, Z. Z.; Xie, Q. Y.; Zhang, W., Finite-time chaos control via nonsingular terminal sliding mode control, Commun Nonlinear Sci Numer Simul, 14, 2728-2733 (2009) · Zbl 1221.37225
[27] Nersesov, Sergey G.; Haddad, Wassim M., Finite-time stabilization of nonlinear impulsive dynamical systems, Nonlinear Anal Hybrid Syst, 2, 832-845 (2008) · Zbl 1223.34089
[28] Guo, R. W.; Vincent, U. E., Finite time stabilization of chaotic systems via single input, Phys Lett A, 375, 119-124 (2010) · Zbl 1241.34054
[29] Pourmahmood, Aghababa Mohammad; Sohrab, Khanmohammadi; Ghassem, Alizadeh, Finite-time synchronization of two different chaotic systems with uncertain parameters via sliding mode technique, Appl Math Modell, 35, 3080-3091 (2011) · Zbl 1219.93023
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