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A unified synchronization criterion for impulsive dynamical networks. (English) Zbl 1194.93090
Summary: This paper focuses on the problem of globally exponential synchronization of impulsive dynamical networks. Two types of impulses are considered: synchronizing impulses and desynchronizing impulses. In previous literature, all of the results are devoted to investigating these two kinds of impulses separately. Thus a natural question arises: Is there any unified synchronization criterion which is simultaneously effective for synchronizing impulses and desynchronizing impulses? In this paper, a unified synchronization criterion is derived for directed impulsive dynamical networks by proposing a concept named “average impulsive interval”. The derived criterion is theoretically and numerically proved to be less conservative than existing results. Numerical examples including scale-free and small-world structures are given to show that our results are applicable to large-scale networks.

MSC:
93C15Control systems governed by ODE
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References:
[1] Arenas, A.; Díaz-Guilera, A.; Kurths, J.; Moreno, Y.; Zhou, C. S.: Synchronization in complex networks, Physics reports 469, No. 3, 93-153 (2008)
[2] Bainov, D.; Simeonov, P. S.: Systems with impulsive effect: stability theory and applications, (1989) · Zbl 0683.34032
[3] Barabási, A.; Albert, R.: Emergence of scaling in random networks, Science 286, No. 5439, 509-512 (1999) · Zbl 1226.05223 · doi:10.1126/science.286.5439.509
[4] Cai, S.; Zhou, J.; Xiang, L.; Liu, Z. R.: Robust impulsive synchronization of complex delayed dynamical networks, Physics letters A 372, No. 30, 4990-4995 (2008) · Zbl 1221.34075 · doi:10.1016/j.physleta.2008.05.077
[5] Chen, W.; Zheng, W. X.: Input-to-state stability and integral input-to-state stability of nonlinear impulsive systems with delays, Automatica 45, No. 6, 1481-1488 (2009) · Zbl 1166.93370 · doi:10.1016/j.automatica.2009.02.005
[6] Chen, W. -H.; Zheng, W. X.: Global exponential stability of impulsive neural networks with variable delay: an lmi approach, IEEE transactions on circuits and systems I 56, No. 6, 1248-1259 (2009)
[7] Chung, F.: Spectral graph theory, (1997) · Zbl 0867.05046
[8] Gao, H.; Lam, J.; Chen, G. R.: New criteria for synchronization stability of general complex dynamical networks with coupling delays, Physics letters A 360, No. 2, 263-273 (2006) · Zbl 1236.34069
[9] Guan, Z.; Hill, D. J.; Yao, J.: A hybrid impulsive and switching control strategy for synchronization of nonlinear systems and application to Chua’s chaotic circuit, International journal of bifurcation and chaos 16, 229-238 (2006) · Zbl 1097.94035 · doi:10.1142/S0218127406014769
[10] Guan, Z.; Hill, D. J.; Shen, X.: On hybrid impulsive and switching systems and application to nonlinear control, IEEE transactions on automatic control 50, No. 7, 1058-1062 (2005)
[11] Hespanha, J., & Morse, A. S. (1999). Stability of switched systems with average dwell-time. In 38th proc. IEEE conf. decision control, Vol. 3 (pp. 2655-2660).
[12] Hespanha, J., Liberzon, D., & Teel, A. R. (2005). On input-to-state stability of impulsive systems. In 44th proc. IEEE conf. decision control (pp. 3992-3997).
[13] Hoppensteadt, F.; Izhikevich, E. M.: Pattern recognition via synchronization in phase-locked loop neural networks, IEEE transactions on neural networks 11, No. 3, 734-738 (2000)
[14] Horn, R.; Johnson, C. R.: Matrix analysis, (1990) · Zbl 0704.15002
[15] Krinsky, V.; Biktashev, V. N.; Efimov, I. R.: Autowave principles for parallel image processing, Physica D 49, No. 1-2, 247-253 (1991)
[16] Li, Z.; Chen, G. R.: Global synchronization and asymptotic stability of complex dynamical networks, IEEE transactions on circuits and systems II 53, No. 1, 28-33 (2006)
[17] Liberzon, D.: Switching in systems and control, (2003) · Zbl 1036.93001
[18] Liu, B., & Hill, D. J. (2007). Robust stability of complex impulsive dynamical systems. In 46th proc. IEEE conf. decision control (pp. 103-108).
[19] Liu, B.; Teo, K. L.; Liu, X.: Robust exponential stabilization for large-scale uncertain impulsive systems with coupling time-delays, Nonlinear analysis 68, No. 5, 1169-1183 (2008) · Zbl 1154.34041 · doi:10.1016/j.na.2006.12.025
[20] Liu, B.; Liu, X. Z.; Chen, G. R.; Wang, H. Y.: Robust impulsive synchronization of uncertain dynamical networks, IEEE transactions on circuits and systems I 52, No. 7, 1431-1441 (2005)
[21] Liu, Y.; Wang, Z.; Liang, J.; Liu, X.: Synchronization and state estimation for discrete-time complex networks with distributed delays, IEEE transactions on systems, man and cybernetics, part B 38, No. 5, 1314-1325 (2008)
[22] Lu, J.; Ho, D. W. C.: Globally exponential synchronization and synchronizability for general dynamical networks, IEEE transactions on systems, man and cybernetics, part B 40, No. 2, 350-361 (2010)
[23] Lu, J.; Ho, D. W. C.; Wu, L. G.: Exponential stabilization in switched stochastic dynamical networks, Nonlinearity 22, 889-911 (2009) · Zbl 1158.93413 · doi:10.1088/0951-7715/22/4/011
[24] Lu, J.; Ho, D. W. C.; Wang, Z. D.: Pinning stabilization of linearly coupled stochastic neural networks via minimum number of controllers, IEEE transactions on neural networks 20, 1617-1629 (2009)
[25] Lu, W.; Chen, T.: New approach to synchronization analysis of linearly coupled ordinary differential systems, Physica D 213, No. 2, 214-230 (2006) · Zbl 1105.34031 · doi:10.1016/j.physd.2005.11.009
[26] Newman, M.; Watts, D. J.: Scaling and percolation in the small-world network model, Physical review E 60, No. 6, 7332-7342 (1999)
[27] Pecora, L.; Carroll, T. L.: Master stability functions for synchronized coupled systems, Physical review letters 80, No. 10, 2109-2112 (1998)
[28] Wang, X.; Chen, G. R.: Synchronization in scale-free dynamical networks: robustness and fragility, IEEE transactions on circuits and systems I 49, No. 1, 54-62 (2002)
[29] Wang, Y.; Wang, H. O.; Xiao, J. W.; Guan, Z. H.: Synchronization of complex dynamical networks under recoverable attacks, Automatica 46, 197-203 (2010) · Zbl 1214.93101 · doi:10.1016/j.automatica.2009.10.024
[30] Wu, C.: Synchronization in networks of nonlinear dynamical systems coupled via a directed graph, Nonlinearity 18, No. 3, 1057-1064 (2005) · Zbl 1089.37024 · doi:10.1088/0951-7715/18/3/007
[31] Wu, C.: Synchronization in complex networks of nonlinear dynamical systems, (2007) · Zbl 1135.34002
[32] Yang, T.: Impulsive systems and control: theory and application, (2001)
[33] Yang, Z.; Xu, D.: Stability analysis of delay neural networks with impulsive effects, IEEE transactions on circuits and systems II 52, No. 8, 517-521 (2005)
[34] Yao, J.; Guan, Z. H.; Hill, D. J.: Passivity-based control and synchronization of general complex dynamical networks, Automatica 45, No. 9, 2107-2113 (2009) · Zbl 1175.93208 · doi:10.1016/j.automatica.2009.05.006
[35] Yu, W.; Chen, G. R.; Lü, J. H.: On pinning synchronization of complex dynamical networks, Automatica 45, 429-435 (2009) · Zbl 1158.93308 · doi:10.1016/j.automatica.2008.07.016
[36] Zhang, G.; Liu, Z.; Ma, Z.: Synchronization of complex dynamical networks via impulsive control, Chaos 17, 043126 (2007) · Zbl 1163.37389 · doi:10.1063/1.2803894
[37] Zhang, H., Guan, Z. H., & Ho, D. W. C. (2006). On synchronization of hybrid switching and impulsive networks. In 45th proc. IEEE conf. decision control (pp. 2765-2770).
[38] Zhang, H.; Guan, Z. H.; Feng, G.: Reliable dissipative control for stochastic impulsive systems, Automatica 44, No. 4, 1004-1010 (2008) · Zbl 1283.93258
[39] Zhang, Q.; Lu, J. A.: Impulsively control complex networks with different dynamical nodes to its trivial equilibrium, Computers and mathematics with applications 57, 1073-1079 (2009) · Zbl 1186.93063 · doi:10.1016/j.camwa.2009.01.002
[40] Zhou, J.; Xiang, L.; Liu, Z.: Synchronization in complex delayed dynamical networks with impulsive effects, Physica A 384, No. 2, 684-692 (2007)
[41] Zou, F.; Nossek, J. A.: Bifurcation and chaos in cellular neural networks, IEEE transactions on circuits and systems I 40, No. 3, 166-173 (1993) · Zbl 0782.92003 · doi:10.1109/81.222797