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Synchronization of a delayed complex dynamical network with free coupling matrix. (English) Zbl 1253.93066

Summary: This paper considers a synchronization problem of a delayed complex dynamical network. For the problem, the virtual target node is chosen as one of nodes in the complex network. It should be pointed out that only one connection is needed between a real target node and a virtual target node instead of \(N\) connections. Moreover, the proposed synchronization scheme does not require additional conditions for coupling matrix unlike the existing works. Based on Lyapunov’s stability theory, a new design criterion for an adaptive feedback controller to achieving synchronization between the real target node and all nodes of the delayed complex network is developed. Finally, the proposed method is applied to a numerical example in order to show the effectiveness of our results.

MSC:

93C40 Adaptive control/observation systems
34D06 Synchronization of solutions to ordinary differential equations
93A14 Decentralized systems
93C15 Control/observation systems governed by ordinary differential equations
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[1] Kim, H.R., Oh, J.J., Kim, D.W.: Task assignment strategies for a complex real-time network system. Int. J. Control. Autom. Syst. 4, 601–614 (2006)
[2] Karimi, H.R.: Robust synchronization and fault detection of uncertain master–slave systems with mixed time-varying delays and nonlinear perturbations. Int. J. Control. Autom. Syst. 9, 671–680 (2011)
[3] Yoo, S.J., Park, J.B., Choi, Y.H.: Adaptive output feedback control of flexible-joint robots using neural networks: dynamic surface design approach. IEEE Trans. Neural Netw. 19, 1712–1726 (2008)
[4] Dou, C.X., Duan, Z.S., Jia, X.B., Niu, P.F.: Study of delay-independent decentralized guaranteed cost control for large scale systems. Int. J. Control. Autom. Syst., 9, 478–488 (2011)
[5] Barahona, M., Pecora, L.M.: Synchronization in small-world systems. Phys. Rev. Lett. 89, 054101 (2002)
[6] Luo, A.C.: A theory for synchronization of dynamical systems. Commun. Nonlinear Sci. Numer. Simul. 14, 1901–1951 (2009) · Zbl 1221.37218
[7] Wang, X.F., Chen, G.: Synchronization in small-world dynamical networks. Int. J. Bifurc. Chaos Appl. Sci. Eng. 12, 187–192 (2002)
[8] 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
[9] Zhou, J., Lu, J.A., Lu, J.: Pinning adaptive synchronization of a general complex dynamical network. Automatica 44, 996–1003 (2008) · Zbl 1283.93032
[10] Yu, W., Chen, W., Lü, J.: On pinning synchronization of complex dynamical networks. Automatica 45, 429–435 (2009) · Zbl 1158.93308
[11] Xiang, L., Zhu, J.J.H.: On pinning synchronization of general coupled networks. Nonlinear Dyn. 64, 339–348 (2011)
[12] Song, Q., Cao, J., Liu, F.: Synchronization of complex dynamical networks with nonidentical nodes. Phys. Lett. A 374, 544–551 (2010) · Zbl 1234.05218
[13] Xu, D., Su, Z.: Synchronization criterions and pinning control of general complex networks with time delay. Appl. Math. Comput. 215, 1593–1608 (2009) · Zbl 1188.34100
[14] Tang, H., Chen, L., Lu, J., Tse, C.K.: Adaptive synchronization between two complex networks with nonidentical topological structures. Physica A 387, 5623–5630 (2008)
[15] Zheng, S., Bi, Q., Cai, G.: Adaptive projective synchronization in complex networks with time-varying coupling delay. Phys. Lett. A 373, 1553–1559 (2009) · Zbl 1228.05267
[16] Wang, L., Dai, H.P., Dong, H., Cao, Y.Y., Sun, X.Y.: Adaptive synchronization of weighted complex dynamical networks through pinning. Eur. Phys. J. B 61, 335–342 (2008)
[17] Strogatz, S.H.: Exploring complex networks. Nature 410, 268–276 (2001) · Zbl 1370.90052
[18] Albert, R., Barabasi, A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002) · Zbl 1205.82086
[19] Wang, X.F., Chen, C.: Complex networks: small-world, scale-free, and beyond. IEEE Circuits Syst. Mag. 3(1), 6–20 (2003)
[20] Xu, S., Feng, G.: Further results on robust adaptive control of uncertain time-delay systems. IET Control Theory Appl. 2, 402–408 (2008)
[21] Xu, S., Lam, J., Zou, Y., Li, J.: Robust admissibility of time-varying singular systems with commensurate time delays. Automatica 45, 2714–2717 (2009) · Zbl 1180.93088
[22] Li, C., Chen, G.: Synchronization in general complex dynamical networks with coupling delays. Physica A 343, 263–278 (2004)
[23] 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
[24] Koo, J.H., Ji, D.H., Won, S.C.: Synchronization of singular complex dynamical networks with time-varying delays. Appl. Math. Comput. 217, 3916–3923 (2010) · Zbl 1203.90170
[25] Liu, H., Lu, J., Lü, J., Hill, D.: Structure identification of uncertain general complex dynamical networks with time delay. Automatica 45, 1799–1807 (2009) · Zbl 1185.93031
[26] Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141 (1963) · Zbl 1417.37129
[27] Boyd, S., Ghaoui, L. El, Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. Philadelphia, SIAM (1994) · Zbl 0816.93004
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