×

Synchronization of singular complex dynamical networks with time-varying delays. (English) Zbl 1203.90170

Summary: This paper considers delay dependent synchronizations of singular complex dynamical networks with time-varying delays. A modified Lyapunov-Krasovskii functional is used to derive a sufficient condition for synchronization in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Numerical examples show the effectiveness of the proposed method.

MSC:

90C35 Programming involving graphs or networks
90B15 Stochastic network models in operations research
90C59 Approximation methods and heuristics in mathematical programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Barahona, M.; Pecora, L. M., Synchronization in small-world systems, Physical Review Letters, 89, 5, 54101 (2002)
[2] Wu, C. W., Synchronizaton in Coupled Chaotic Circuits and Systems (2002), World Scientfic Pub. Co. Inc.
[3] Luo, A. C.J., A theory for synchronization of dynamical systems, Communications in Nonlinear Science and Numerical Simulation, 14, 5, 1901-1951 (2009) · Zbl 1221.37218
[4] Wang, X.; Chen, G., Synchronization in small-world dynamical networks, International Journal of Bifurcation and Chaos, 12, 1, 187-192 (2002)
[6] Li, C.; Chen, G., Synchronization in general complex dynamical networks with coupling dylays, Physica A: Statistical Mechanics and its Applications, 343, 263-278 (2004)
[7] Lu, J.; Chen, G., A time-varying complex dynamical network model and its comtrolled synchronization criteria, IEEE Transactions on Automatic Control, 50, 6, 841-846 (2005) · Zbl 1365.93406
[8] Zhou, Jin; Lu, Jun an; Lu, Jinhu, Adaptive synchronization of an uncertain complex dynamical network, IEEE Transactions on Automatic Control, 51, 4, 652-656 (2006) · Zbl 1366.93544
[9] Zhang, Qunjiao; Lu, Junan; Lu, Jinhu; Tse, C. K., Adaptive feedback synchronization of a general complex dynamical network with delayed nodes, IEEE Transactions on Circuits and Systems - II, 55, 2, 183-187 (2008)
[10] Li, K.; Guan, S.; Gong, X.; Lai, C. H., Synchronization stability of general complex dynamical networks with time-varying delays, Physics Letters A, 372, 48, 7133-7139 (2008) · Zbl 1226.05232
[11] Xiong, W.; Ho, D. W.C.; Cao, J., Synchronization analysis of singular hybrid coupled networks, Physics Letters A, 372, 44, 6633-6637 (2008) · Zbl 1225.34062
[12] Gu, K.; Kharitonov, V.; Chen, J., Stability of Time-Delay Systems (2003), Birkhaüser · Zbl 1039.34067
[13] Skelton, R. E.; Iwasaki, T.; Grigoriadis, K. M., A Unified Algebraic Approach to Linear Control Design (1997), CRC
[14] Yakubovich, V. A., S-procedure in nonlinear control theory, Vestnik Leningrad University, 1, 62-77 (1971) · Zbl 0232.93010
[15] Xu, Shengyuan; Van Dooren, P.; Stefan, R.; Lam, J., Robust stability and stabilization for singular systems with state delaay and parameter uncertainty, IEEE Transactions on Automatic Control, 47, 7, 1122-1128 (2002) · Zbl 1364.93723
[16] Lu, Guoping; Ho, D. W.C., Generalized quadratic stability for continuous-time singular systems with nonlinear perturbation, IEEE Transactions on Automatic Control, 51, 5, 818-823 (2006) · Zbl 1366.34015
[17] Xu, D.; Su, Z., Synchronization criterions and pinning control of general complex networks with time delay, Applied Mathematics and Computation, 215, 4, 1593-1608 (2009) · Zbl 1188.34100
[18] Park, J. H.; Lee, S. M.; Jung, H. Y., LMI optimization approach to synchronization of stochastic delayed discrete-time complex networks, Journal of Optimization Theory and Applications, 143, 2, 357-367 (2009) · Zbl 1175.90085
[19] Ji, D. H.; Park, J. H.; Yoo, W. J.; Won, S. C.; Lee, S. M., Synchronization criterion for Lur’e type complex dynamical networks with time-varying delay, Physics Letters A, 374, 10, 1218-1227 (2010) · Zbl 1236.05186
[20] Sun, Wen; Chen, Zhong; Lü, Yibing; Chen, Shihua, An intriguing hybrid synchronization phenomenon of two coupled complex networks, Applied Mathematics and Computation, 216, 8, 2301-2309 (2010) · Zbl 1203.93163
[21] Lee, S. M.; Ji, D. H.; Park, J. H.; Won, S. C., \(H_∞\) synchronization of chaotic systems via dynamic feedback approach, Physics Letters A, 372, 29, 4905-4912 (2008) · Zbl 1221.93087
[22] Li, Hongjie; Yue, Dong, Synchronization stability of general complex dynamical networks with time-varying delays: a piecewise analysis method, Neurocomputing, 232, 2, 149-158 (2009) · Zbl 1178.34095
[23] Yue, Dong; Li, Hongjie, Synchronization stability of continuous/discrete complex dynamical networks with interval time-varying delays, Neurocomputing, 73, 4-6, 809-819 (2010)
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.