Guaranteed cost synchronization of a complex dynamical network via dynamic feedback control. (English) Zbl 1238.93070

Summary: In this paper, the problem of guaranteed cost synchronization for a complex network is investigated. In order to achieve the synchronization, two types of guaranteed cost dynamic feedback controllers are designed. Based on Lyapunov’s stability theory, a Linear Matrix Inequality (LMI) convex optimization problem is formulated to find the controller which guarantees the asymptotic stability and minimizes the upper bound of a given quadratic cost function. Finally, a numerical example is given to illustrate the proposed method.


93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93D20 Asymptotic stability in control theory
93B52 Feedback control
90C22 Semidefinite programming
Full Text: DOI


[1] Strogatz, S.H., Exploring 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] Kim, H.R.; Oh, J.J.; Kim, D.W., Task assignment strategies for a complex real-time network system, International journal of control, automation, and systems, 4, 601-614, (2006)
[5] Barahona, M.; Pecora, L.M., Synchronization in small-world systems, Phys. rev. lett., 89, 054101, (2002)
[6] Karimi, H.R., Robust synchronization and fault detection of uncertain master-slave systems with mixed time-varying delays and nonlinear perturbations, International journal of control, automation, and systems, 9, 671-680, (2011)
[7] 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, 1218-1227, (2010) · Zbl 1236.05186
[8] Li, N.; Zhang, Y.; Hu, J.; Nie, Z., Synchronization for general complex dynamical networks with sampled-data, Neurocomputing, 74, 805-811, (2011)
[9] 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 computation, 218, 9, 4872-4880, (2012) · Zbl 1238.93053
[10] Li, R.; Duan, Z.S.; Chen, G.R., Cost and effect of pinning control for network synchronization, Chinese physics B, 18, 1056-1674, (2009)
[11] Maurizio, P.; Mario, B., Criteria for global pinning-controllability of complex networks, Automatica, 44, 3100-3106, (2008) · Zbl 1153.93329
[12] 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: regular papers, 53, 2739-2745, (2006) · Zbl 1374.37128
[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, Physics letters A, 373, 1553-1559, (2009) · Zbl 1228.05267
[16] 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
[17] Chang, S.S.L.; Peng, T.K.C., Adaptive guaranteed cost control of systems with uncertain parameters, IEEE trans. automat. control, 17, 4, 474-483, (1972) · Zbl 0259.93018
[18] Petersen, I.R.; McFarlane, D.C., Optimal guaranteed cost control and filtering for uncertain linear systems, IEEE trans. automat. control, 39, 9, 1971-1977, (1994) · Zbl 0817.93025
[19] Petersen, I.R., Guaranteed cost LQG control of uncertain linear systems, IEE proc. control theory appl., 142, 2, 95-102, (1995) · Zbl 0822.93063
[20] Park, J.H., Guaranteed cost stabilization of neutral differential systems with parametric uncertainty, Journal of computational and applied mathematics, 151, 371-382, (2003) · Zbl 1038.93044
[21] Park, J.H.; Jung, H.Y.; Park, J.I.; Lee, S.G., Decentralized dynamic output feedback controller design for guaranteed cost stabilization of large-scale discrete-delay systems, Applied mathematics and computation, 156, 307-320, (2004) · Zbl 1108.93007
[22] Xiao, X.; Mao, Z., Decentralized guaranteed cost stabilization of time-delay large-scale systems base don reduced-order observers, Journal of the franklin institute, 348, 2689-2700, (2011) · Zbl 1239.93109
[23] Dou, C.X.; Duan, Z.S.; Jia, X.B.; Niu, P.F., Study of delay-independent decentralized guaranteed cost control for large scale systems, International journal of control, automation, and systems, 9, 478-488, (2011)
[24] Park, J.H., Convex optimization approach to dynamic output feedback control for delay differential systems of neutral type, Journal of optimization theory and applications, 127, 411-423, (2005) · Zbl 1113.93048
[25] Boyd, B.; Ghaoui, L.E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in systems and control theory, (1994), SIAM Philadelphia
[26] Scherer, C.; Gahinet, P.; Chilali, M., Multiobjective output-feedback control via LMI optimization, IEEE transactions on automatic control, 42, 896-911, (1997) · Zbl 0883.93024
[27] Chua, L.O.; Komuro, M.; Matsumoto, T., The double scroll family, IEEE transactions on circuits and systems I, 33, 1072-1118, (1986) · Zbl 0634.58015
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.