Li, Kun; Guan, Shuguang; Gong, Xiaofeng; Lai, C.-H. Synchronization stability of general complex dynamical networks with time-varying delays. (English) Zbl 1226.05232 Phys. Lett., A 372, No. 48, 7133-7139 (2008). Summary: The synchronization problem of some general complex dynamical networks with time-varying delays is investigated. Both time-varying delays in the network couplings and time-varying delays in the dynamical nodes are considered. The novel delay-dependent criteria in terms of linear matrix inequalities (LMI) are derived based on free-weighting matrices technique and appropriate Lyapunov functional proposed recently. Numerical examples are given to illustrate the effectiveness and advantage of the proposed synchronization criteria. Cited in 30 Documents MSC: 05C82 Small world graphs, complex networks (graph-theoretic aspects) 34B45 Boundary value problems on graphs and networks for ordinary differential equations 34D06 Synchronization of solutions to ordinary differential equations 34D20 Stability of solutions to ordinary differential equations 15A30 Algebraic systems of matrices Keywords:complex network; time-varying delay; synchronization; linear matrix inequality PDFBibTeX XMLCite \textit{K. Li} et al., Phys. Lett., A 372, No. 48, 7133--7139 (2008; Zbl 1226.05232) Full Text: DOI References: [1] Strogatz, S. H., Nature, 410, 268 (2001) [2] Albert, R.; Barabasi, A.-L., Rev. Mod. Phys., 74, 47 (2002) [3] Hong, H.; Choi, M. Y.; Kim, B. J., Phys. Rev. E, 65, 26 (2002) [4] Wu, C. W., IEEE Trans. AC, 51, 1207 (2006) [5] Li, Z.; Chen, G., IEEE Trans. CAS-II, 53, 28 (2006) [6] Li, K.; Lai, C.-H., Phys. Lett. A, 372, 1601 (2008) [7] Wang, X. F.; Chen, G., Physica A, 310, 521 (2002) [8] Wang, X. F.; Chen, G., IEEE Trans. CAS-I, 49, 54 (2002) [9] Li, C. G.; Chen, G., Physica A, 343, 263 (2004) [10] Gao, H.; Lam, J.; Chen, G., Phys. Lett. A, 360, 263 (2006) [11] Lü, J.; Chen, G., IEEE Trans. AC, 50, 841 (2005) [12] Zhou, J.; Lu, J.; Lü, J., IEEE Trans. AC, 51, 652 (2006) [13] Sorrentina, F.; di Bernardo, M.; Garofalo, F.; Chen, G., Phys. Rev. E, 75, 046103 (2007) [14] Zhang, Q.; Lu, J.; Lü, J.; Tse, C., IEEE Trans. CAS-II, 55, 183 (2008) [15] Zhou, J.; Chen, T., IEEE Trans. CAS-I, 53, 733 (2006) [16] Zhou, J.; Xiang, L.; Liu, Z., Physica A, 385, 729 (2007) [17] Fridman, E.; Shaked, U., Int. J. Control, 76, 48 (2003) · Zbl 1023.93032 [18] Park, P., IEEE Trans. AC, 44, 876 (1999) [19] Moon, Y. S.; Park, P.; Kwonm, W. H.; Lee, Y. S., Int. J. Control, 74, 1447 (2001) [20] He, Y.; Wu, M.; She, J. H.; Liu, G. P., IEEE Trans. AC, 49, 828 (2004) [21] Wu, M.; He, Y.; She, J. H.; Liu, G. P., Automatica, 40, 1435 (2004) [22] He, Y.; Wu, M.; She, J. H.; Liu, G. P., Syst. Control Lett., 51, 57 (2004) [23] Wu, M.; He, Y.; She, J. H., IEEE Trans. AC, 49, 2266 (2004) [24] He, Y.; Wang, W.; Xie, L.; Lin, C., IEEE Trans. AC, 52, 293 (2007) [25] Barabsi, A. L.; Albert, R., Science, 285, 509 (1999) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.