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Global synchronization stability for stochastic complex dynamical networks with probabilistic interval time-varying delays. (English) Zbl 1252.90079
Authors’ abstract: The synchronization problem for a class of complex dynamical networks with stochastic disturbances and probabilistic interval time-varying delays is investigated. Based on the stochastic analysis techniques and properties of the Kronecker product, some delay-dependent asymptotical synchronization stability criteria are derived in the form of linear matrix inequalities (LMIs). The solvability of derived conditions depends not only on the size of the delay, but also on the probability of Bernoulli stochastic variables. A numerical example is given to illustrate the feasibility and effectiveness of the proposed method.
90C31Sensitivity, stability, parametric optimization
90B15Network models, stochastic (optimization)
[1]Aldana, M.: Boolean dynamics of networks with scale-free topology. Physica D. Nonlinear Phenom. 185, 45–66 (2003) · Zbl 1039.94016 · doi:10.1016/S0167-2789(03)00174-X
[2]Dangalchev, C.: Generation models for scale-free networks. Physica A. Stat. Mech. Appl. 338, 659–671 (2004) · doi:10.1016/j.physa.2004.01.056
[3]Li, Z., Chen, G.: Global synchronization and asymptotic stability of complex dynamical networks. IEEE Trans. Circuits Syst. II, Express Briefs 53, 28–33 (2006) · doi:10.1109/TCSII.2005.854315
[4]Liang, J., Wang, Z., Liu, X.: Exponential synchronization of stochastic delayed discrete-time complex networks. Nonlinear Dyn. 53, 153–165 (2008) · Zbl 1172.92002 · doi:10.1007/s11071-007-9303-5
[5]Wang, X., Chen, G.: Complex networks: small-world, scale-free and beyond. IEEE Circuits Syst. Mag. 3, 6–20 (2003) · doi:10.1109/MCAS.2003.1228503
[6]Gao, H., Lam, J., Chen, G.: New criteria for synchronization stability of general complex dynamical networks with coupling delays. Phys. Lett. A 360, 263–273 (2006) · Zbl 1236.34069 · doi:10.1016/j.physleta.2006.08.033
[7]Li, C., Sun, W., Kurths, J.: Synchronization of complex dynamical networks with time delays. Physica A. Stat. Mech. Appl. 361, 24–34 (2006) · doi:10.1016/j.physa.2005.07.007
[8]Liu, X., Chen, T.: Exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling. Physica A. Stat. Mech. Appl. 381, 82–92 (2007) · doi:10.1016/j.physa.2007.03.026
[9]Wang, Y., Wang, Z., Liang, J.: A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances. Phys. Lett. A 372, 6066–6073 (2008) · Zbl 1223.90013 · doi:10.1016/j.physleta.2008.08.008
[10]Wang, Y., Wang, Z., Liang, J.: Global synchronization for delayed complex networks with randomly occurring nonlinearities and multiple stochastic disturbances. J. Phys. A, Math. Theor. 42, 135101–135111 (2009) · Zbl 1159.90013 · doi:10.1088/1751-8113/42/13/135101
[11]Cao, J., Lu, J.: Adaptive synchronization of neural networks with or without time-varying delay. Chaos. Interdiscip. J. Nonlinear Sci. 16, 013133–013143 (2006) · Zbl 1144.37331 · doi:10.1063/1.2178448
[12]Jiang, Y.: Globally coupled maps with time delay interactions. Phys. Lett. A 267, 342–349 (2000) · doi:10.1016/S0375-9601(00)00135-3
[13]Lu, W., Chen, T.: Synchronization analysis of linearly coupled networks of discrete time systems. Physica D. Nonlinear Phenom. 198, 148–168 (2004) · Zbl 1071.39011 · doi:10.1016/j.physd.2004.08.024
[14]Duan, Z., Chen, G., Huang, L.: Synchronization of weighted networks and complex synchronized regions. Phys. Lett. A 372, 3741–3751 (2008) · Zbl 1220.34074 · doi:10.1016/j.physleta.2008.02.056
[15]Yu, W., Cao, J., Lu, J.: Global synchronization of linearly hybrid coupled networks with time-varying delay. SIAM J. Appl. Dyn. Syst. 7, 108–133 (2008) · Zbl 1161.94011 · doi:10.1137/070679090
[16]Hua, C., Wang, Q., Guan, X.: Global adaptive synchronization of complex networks with nonlinear delay coupling interconnections. Phys. Lett. A 368, 281–288 (2007) · Zbl 1209.93083 · doi:10.1016/j.physleta.2007.04.019
[17]Li, Z., Jiao, L., Lee, J.: Robust adaptive global synchronization of complex dynamical networks by adjusting time-varying coupling strength. Physica A. Stat. Mech. Appl. 387, 1369–1380 (2008) · doi:10.1016/j.physa.2007.10.063
[18]Wang, Z., Liu, Y., Li, M., Liu, X.: Stability analysis for stochastic Cohen–Grossberg neural networks with mixed time delays. IEEE Trans. Neural Netw. 17, 814–820 (2006) · doi:10.1109/TNN.2006.872355
[19]Liang, J., Wang, Z., Liu, Y., Liu, X.: Global synchronization control of general delayed discrete-time networks with stochastic coupling and disturbances. IEEE Trans. Syst. Man Cybern., Part B 38, 1073–1083 (2008) · doi:10.1109/TSMCB.2008.925724
[20]Sun, Y., Cao, J., Wang, Z.: Exponential synchronization of stochastic perturbed chaotic delayed neural networks. Neurocomputing 70, 2477–2485 (2007) · doi:10.1016/j.neucom.2006.09.006
[21]Cao, J., Li, P., Wang, W.: Global synchronization in arrays of delayed neural networks with constant and delayed coupling. Phys. Lett. A 353, 318–325 (2006) · doi:10.1016/j.physleta.2005.12.092
[22]Wang, Z., Liu, Y., Liu, X.: Hfiltering for uncertain stochastic time-delay systems with sector-bounded nonlinearities. Automatica 44, 1268–1277 (2008) · doi:10.1016/j.automatica.2007.09.016
[23]Wang, S., Nathuji, R., Bettati, R., Zhao, W.: Providing statistical delay guarantees in wireless networks. In: International Conference on Distributed Computing Systems, vol. 24, pp. 48–57 (2004)
[24]Luo, R., Chung, L.: Stabilization for linear uncertain system with time latency. IEEE Trans. Ind. Electron. 49, 905–910 (2002) · doi:10.1109/TIE.2002.801243
[25]Moon, Y., Park, P., Kwon, W.: Robust stabilization of uncertain input-delayed systems using reduction method. Automatica 37, 307–312 (2001) · Zbl 0969.93035 · doi:10.1016/S0005-1098(00)00145-X
[26]Park, H., Kim, Y., Kim, D., Kwon, W.: A scheduling method for network-based control systems. IEEE Trans. Control Syst. Technol. 10, 318–330 (2002) · doi:10.1109/87.998012
[27]Yue, D., Tian, E., Zhang, Y., Peng, C.: Delay-distribution-dependent robust stability of uncertain systems with time-varying delay. Int. J. Robust Nonlinear Control 19, 377–393 (2009) · Zbl 1157.93478 · doi:10.1002/rnc.1314
[28]Zhang, Y., Yue, D., Tian, E.: Robust delay-distribution-dependent stability of discrete-time stochastic neural networks with time-varying delay. Neurocomputing 72, 1265–1273 (2009) · Zbl 05718924 · doi:10.1016/j.neucom.2008.01.028
[29]Wang, Z., Ho, D., Liu, X.: Robust filtering under randomly varying sensor delay with variance constraints. IEEE Trans. Circuits Syst. II, Express Briefs 51, 320–326 (2004) · doi:10.1109/TCSII.2004.829572
[30]Wu, M., He, Y., She, J., Liu, G.: Delay-dependent criteria for robust stability of time-varying delay systems. Automatica 40, 1435–1439 (2004) · Zbl 1059.93108 · doi:10.1016/j.automatica.2004.03.004
[31]Xu, S., Lam, J., Zou, Y.: New results on delay-dependent robust Hcontrol for systems with time-varying delays. Automatica 42, 343–348 (2006) · Zbl 1099.93010 · doi:10.1016/j.automatica.2005.09.013
[32]Yang, F., Wang, Z., Hung, Y., Gani, M.: Hcontrol for networked systems with random communication delays. IEEE Trans. Autom. Control 51, 511–518 (2006) · doi:10.1109/TAC.2005.864207
[33]Yu, W., Cao, J., Lu, J.: Global synchronization of linearly hybrid coupled networks with time-varying delay. SIAM J. Appl. Dyn. Syst. 7, 108–133 (2008) · Zbl 1161.94011 · doi:10.1137/070679090
[34]Langville, A., Stewart, W.: The Kronecker product and stochastic automata networks. J. Comput. Appl. Math. 167, 429–447 (2004) · Zbl 1104.68062 · doi:10.1016/j.cam.2003.10.010
[35]Mao, X.: Exponential stability of stochastic delay interval systems with Markovian switching. IEEE Trans. Autom. Control 47, 1604–1612 (2002) · doi:10.1109/TAC.2002.803529
[36]Wu, M., He, Y., She, J., Liu, G.: Delay-dependent criteria for robust stability of time-varying delay systems. Automatica 40, 1435–1439 (2004) · Zbl 1059.93108 · doi:10.1016/j.automatica.2004.03.004
[37]Xu, S., Lam, J.: Improved delay-dependent stability criteria for time-delay systems. IEEE Trans. Autom. Control 50, 384–387 (2005) · doi:10.1109/TAC.2005.843873
[38]Yue, D., Han, Q.: Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching. IEEE Trans. Autom. Control 50, 217–222 (2005) · doi:10.1109/TAC.2004.841935