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Exponential synchronization for complex dynamical networks with sampled-data. (English) Zbl 1264.93013
Summary: This paper is concerned with the problem of exponential synchronization for a kind of Complex Dynamical Networks (CDNs) with time-varying coupling delay and sampled-data. The sampling period considered here is assumed to be time-varying but bounded. A newly exponential synchronization condition is provided by using the Lyapunov method. Based on the condition, a set of sampled-data synchronization controllers is designed in terms of the solution of Linear Matrix Inequalities (LMIs) that can be solved effectively by using available software. The derived results are theoretically and numerically proved to be less conservative than the existing results. Two numerical examples are introduced to show the effectiveness and improvement of the given results.

93A15 Large-scale systems
93C57 Sampled-data control/observation systems
93C15 Control/observation systems governed by ordinary differential equations
Full Text: DOI
[1] Li, C.; Chen, G., Synchronization in general complex dynamical networks with coupling delays, Physica A, 343, 263-278, (2004)
[2] Lu, J.; Ho, D.W.C., Globally exponential synchronization and synchronizability for general dynamical networks, IEEE transactions on systems, man, and cybernetics, part bcybernetics, 40, 350-361, (2010)
[3] Wang, Z.; Wang, Y.; Liu, Y., Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time-delays, IEEE transactions on neural networks, 21, 11-25, (2010)
[4] Wang, Y.; Xiao, J.; Wang, H.O., Global synchronization of complex dynamical networks with network failures, International journal of robust and nonlinear control, 20, 1667-1677, (2010) · Zbl 1204.93061
[5] Cao, J.; Li, P.; Wei, W., Global synchronization in arrays of delayed neural networks with constant and delayed coupling, Physics letters A, 353, 318-325, (2006)
[6] Lu, J.; Ho, D.W.C.; Cao, J., A unified synchronization criterion for impulsive dynamical networks, Automatica, 46, 1215-1221, (2010) · Zbl 1194.93090
[7] Lee, T.H.; Park, Ju H.; Ji, D.; Kwon, O.M.; Lee, S.M., Guaranteed cost synchronization of a complex dynamical network via dynamic feedback control, Applied mathematics and computation, 218, 6469-6481, (2012) · Zbl 1238.93070
[8] Zhou, W.; Wang, T.; Mou, J.; Fang, J., Mean square exponential synchronization in Lagrange sense for uncertain complex dynamical networks, Journal of the franklin institute, 349, 1267-1282, (2012) · Zbl 1273.93017
[9] Xu, Y.; Zhou, W.; Fang, J.; Sun, W.; Pan, L., Topology identification and adaptive synchronization of uncertain complex networks with non-derivative and derivative coupling, Journal of the franklin institute, 347, 1566-1576, (2010) · Zbl 1202.93023
[10] Park, M.J.; Kwon, O.M.; Park, JuH.; Lee, S.M.; Cha, E.J., Synchronization criteria for coupled stochastic neural networks with time-varying delays and leakage delay, Journal of the franklin institute, 348, 1699-1720, (2012) · Zbl 1254.93012
[11] Huang, C.; Ho, D.W.C.; Lu, J., Synchronization analysis of a complex network family, Nonlinear analysisreal world applications, 11, 1933-1945, (2010) · Zbl 1188.93009
[12] Shen, B.; Wang, Z.; Liu, X., Bounded \(\mathcal{H}_\infty\) synchronization and state estimation for discrete time-varying stochastic complex networks over a finite-horizon, IEEE transactions on neural networks, 22, 145-157, (2010)
[13] Shi, P., Robust filtering for uncertain delay systems under sampled measurements, Signal processing, 58, 131-151, (1996) · Zbl 0901.93068
[14] Fridman, E.; Seuret, A.; Richard, J.P., Robust sampled-data stabilization of linear systemsan input delay approach, Automatica, 40, 1441-1446, (2004) · Zbl 1072.93018
[15] Liu, M.; You, J.; Ma, X., \(\mathcal{H}_\infty\) filtering for sampled-data stochastic systems with limited capacity channel, Signal processing, 91, 1826-1837, (2010) · Zbl 1217.93167
[16] Wen, J.; Liu, F.; Nguang, S.K., Sampled-data predictive control for uncertain jump systems with partly unknown jump rates and time-varying delay, Journal of the franklin institute, 349, 305-322, (2012) · Zbl 1254.93110
[17] Gao, H.; Wu, J.; Shi, P., Robust sampled-data \(\mathcal{H}_\infty\) control with stochastic sampling, Automatica, 45, 1729-1736, (2009) · Zbl 1184.93039
[18] Li, N.; Zhang, Y.; Hu, J.; Nie, Z., Synchronization for general complex dynamical networks with sampled-data, Neurocomputing, 74, 805-811, (2011)
[19] Wang, Z.; Liu, Y.; Liu, X., \(\mathcal{H}_\infty\) filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities, Automatica, 44, 1268-1277, (2008) · Zbl 1283.93284
[20] Shu, Z.; Lam, J., Exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays, International journal of control, 81, 865-882, (2008) · Zbl 1152.93462
[21] Shao, H., New delay-dependent stability criteria for systems with interval delay, Automatica, 45, 744-749, (2009) · Zbl 1168.93387
[22] Liu, Y.; Wang, Z.; Liu, X., Global exponential stability of generalized recurrent neural networks with discrete and distributed delays, Neural networks, 19, 667-675, (2006) · Zbl 1102.68569
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