×

Synchronization of a complex dynamical network with coupling time-varying delays via sampled-data control. (English) Zbl 1291.34120

Summary: The synchronization problem of a complex dynamical network with coupling time-varying delays via delayed sampled-data controller is investigated. In order to make full use of the sawtooth structure characteristic of the sampling input delay, a discontinuous Lyapunov functional is proposed based on the Extended Wirtinger Inequality. From a convex representation of the sector-restricted nonlinearity in system dynamics, the stability condition based on Lyapunov stability theory is obtained by utilization of linear matrix inequality formulation to find the controller which achieves the synchronization of a complex dynamical network with coupling time-varying delay. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.

MSC:

34K25 Asymptotic theory of functional-differential equations
34K35 Control problems for functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Strogatz, S. H., Eaxploring complex networks, Nature, 410, 268-276 (2001) · Zbl 1370.90052
[2] Dorogovtesev, S. N.; Mendes, J. F.F., Evolution of networks, Advances in Physics, 51, 1079-1187 (2002)
[3] Newman, M. E.J., The structure and function of complex networks, SIAM Review, 45, 167-256 (2003) · Zbl 1029.68010
[4] Ji, D. H.; Jeong, S. C.; Park, JuH.; Lee, S. M.; Won, S. C., Adaptive lag synchronization for uncertain complex dynamical network with delayed coupling, Applied Mathematics and Computation, 218, 4872-4880 (2012) · Zbl 1238.93053
[5] Zhou, J.; Chen, T., Synchronization in general complex delayed dynamical networks, IEEE Transactions on Circuits and Systems I, 53, 733-744 (2006) · Zbl 1374.37056
[6] Wang, B.; Guan, Z. H., Chaos synchronization in general complex dynamical network with coupling delays, Nonlinear Analysis: Real World Applications, 11, 1925-1932 (2010) · Zbl 1188.93096
[7] Li, H.; Yue, D., Synchronization stability of general complex dynamical networks with time-varying delays: A piecewise analysis method, Journal of Computational and Applied Mathematics, 232, 149-158 (2009) · Zbl 1178.34095
[8] Ji, D. H.; Park, Ju. 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, 1218-1227 (2010) · Zbl 1236.05186
[9] Zheng, S.; Dong, G.; Bi, Q., Impulsive synchronization of complex networks with non-delayed and delayed coupling, Physics Letters A, 373, 4255-4259 (2009) · Zbl 1234.05220
[10] Jiang, G. P.; Tang, W. K.S.; Chen, G., A state-observer-based approach for synchronization in complex dynamical networks, IEEE Transactions on Circuits and Systems I, 53, 2739-2745 (2006) · Zbl 1374.37128
[11] Liu, S.; Li, X.; Jiang, W.; Fan, Y. Z., Adaptive synchronization in complex dynamical networks with coupling delays for general graphs, Applied Mathematics and Computation (2011)
[12] Maurizio, P.; Mario, B., Criteria for global pinning-contollability of complex networks, Automatica, 44, 3100-3106 (2008) · Zbl 1153.93329
[13] Xu, D.; Su, Z., Synchronization criterions and pinning control of general complex networks with time delay, Applied Mathematics and Conputation, 215, 1593-1608 (2009) · Zbl 1188.34100
[14] Liu, H.; Lu, J. A.; Lü, J.; Hill, D. J., Structure identification of uncertain general complex dynamical networks with time delay, Automatica, 45, 1799-1807 (2009) · Zbl 1185.93031
[15] Wang, G.; Cao, J.; Ju, J., Outer synchronization between two nonidentical networks with circumstance noise, Physica A, 389, 1480-1488 (2010)
[16] Ji, D. H.; Jeong, S. C.; Park, J. H.; Lee, S. M.; Won, S. C., Adaptive lag synchronization for uncertain complex dynamical network with delayed coupling, Applied Mathematics and Conputation, 218, 4872-4880 (2012) · Zbl 1238.93053
[17] Zhang, Q.; Niu, Y.; Wang, L.; Shen, L.; Zhu, H., Average consensus seeking of high-order continuous-time multi-agent systems with multiple time-varying communication delays, International Journal of Control, Automation, and Systems, 9, 1209-1218 (2011)
[18] Park, M. J.; Kwon, O. M.; Park, J. H.; Lee, S. M.; Cha, E. J., Synchronization criteria for coupled neural networks with interval time-varying delays and leakage delay, Applied Mathematics and Computation, 218, 6762-6775 (2012) · Zbl 1401.93021
[19] Kwon, O. M.; Lee, S. M.; Park, J. H.; Cha, E. J., New approaches on stability criteria for neural networks with interval time-varying delays, Applied Mathematics and Computation, 218, 9953-9964 (2012) · Zbl 1253.34066
[20] Wu, Z. G.; Park, Ju. H.; Su, H.; Chu, J., Admissibility and dissipativity analysis for discrete-time singular systems with mixed time-varying delays, Applied Mathematics and Computation, 218, 7128-7138 (2012) · Zbl 1243.93066
[21] Ahmed, A.; Rehan, M.; Iqbal, N., Incorporating anti-windup gain in improving stability of actuator constrained linear multiple state delays systems, International Journal of Control, Automation, and Systems, 9, 681-690 (2011)
[22] Mikheev, Y.; Sobolev, V.; Fridman, E., Asymptotic analysis of digital control systems, Automation and Remote Control, 49, 1175-1180 (1988) · Zbl 0692.93046
[23] Astrom, K.; Wittenmark, B., Adaptive Control (1989), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0697.93033
[24] Fridman, E.; Shaked, U.; Suplin, V., Input/output delay approach to robust sampled-data \(H_\infty\) control, Systems and Control Letters, 54, 271-282 (2005) · Zbl 1129.93371
[25] Lam, H. K.; Ling, W. K., Sampled-data fuzzy controller for continuous nonlinear systems, IET Control Theory Applications, 2, 32-39 (2008)
[26] Lu, J. G., Chaotic behavior in sampled-data control systems with saturating control, Chaos, Solitons and Fractals, 30, 147-155 (2006) · Zbl 1220.93048
[27] Peng, C.; Han, Q. L.; Yue, D.; Tian, E., Sampled-data robust \(H_\infty\) control for T-S fuzzy systems with time delay and uncertainties, Fuzzy Sets and Systems, 179, 20-33 (2011) · Zbl 1235.93147
[28] Zhang, C. K.; He, Y.; Wu, M., Exponential synchronization of neural networks with time-varying mixed delays and sampled-data, Neurocomputing, 74, 265-273 (2010)
[29] Li, N.; Zhang, Y.; Hu, J.; Nie, Z., Synchronization for general complex dynamical networks with sampled-data, Neurocomputing, 74, 805-811 (2011)
[30] Boyd, B.; Ghaoui, L. E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in systems and control theory (1994), SIAM: SIAM Philadelphia
[31] Chua, L. O.; Komuro, M.; Matsumoto, T., The Double Scroll Family, IEEE Transactions on Cirtuis and Systems, I, 33, 1072-1118 (1986) · Zbl 0634.58015
[32] Jiang, Z. P.; Kanellakopoulos, I., Global output-feedback tracking for a benchmark nonlinear system, IEEE Transactions on Automatic Control, 45, 1023-1027 (2000) · Zbl 0968.93531
[33] Gu, K.; Kharitonov, V. K.; Chen, J., Stability of time-delay systems (2003), Birkhauser: Birkhauser Boston
[34] Liu, K.; Suplin, V.; Fridman, E., Stability of linear systems with general sawtooth delay, IMA Journal of Mathematical Control and Information, 27, 419-436 (2011) · Zbl 1206.93080
[35] Liu, K.; Fridman, E., Wirtinger’s inequality and Lyapunov-based sampled-data stabilization, Automatica, 48, 102-108 (2012) · Zbl 1244.93094
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.