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Stabilization of complex dynamical networks with noise disturbance under performance constraint. (English) Zbl 1246.37100
Summary: Under given performance constraint, this paper studies the stabilization problem of general dynamical network subject to noise disturbance. The newly presented dynamical network model includes both intrinsic disturbance of single node and communication noise over the network connections, which appear typically in a network environment. Single controller is pinned into one of the nodes for the exponential stabilization of dynamical network, and the prescribed performance constraint is satisfied. The reason why only one controller is valid for stabilization of dynamical network is the full utilization of network’s local connections. One important feature of this paper is the introduction of the performance constraint concept into the stabilization of complex dynamical network with intrinsic and communication noises. The derived criteria are expressed in terms of linear matrix inequalities (LMIs), which are easy to be verified by resorting to recently developed algorithm. Numerical example is utilized to illustrate the effectiveness of the proposed results.

37N35Dynamical systems in control
93D15Stabilization of systems by feedback
Full Text: DOI
[1] Wu, C. W.: Synchronization in networks of nonlinear dynamical systems coupled via a directed graph, Nonlinearity 18, No. 3, 1057-1064 (2005) · Zbl 1089.37024 · doi:10.1088/0951-7715/18/3/007
[2] Cao, J. D.; Chen, G. R.; Li, P.: Global synchronization in an array of delayed neural networks with hybrid coupling, IEEE transactions on systems, man and cybernetics, part B 38, No. 2, 488-498 (2008)
[3] Pecora, L. M.; Carroll, T. L.: Master stability functions for synchronized coupled systems, Physical review letters 80, No. 10, 2109-2112 (1998)
[4] Wang, X. F.; Chen, G. R.: Synchronization in scale-free dynamical networks: robustness and fragility, IEEE transactions on circuits and systems I 49, No. 1, 54-62 (2002)
[5] Huang, C.; Ho, D. W. C.; Lu, J. Q.: Synchronization analysis of complex network family, Nonlinear analysis series B: real world applications 11, No. 3, 1933-1945 (2010) · Zbl 1188.93009 · doi:10.1016/j.nonrwa.2009.04.016
[6] Lu, J. Q.; Ho, D. W. C.; Wu, L. G.: Exponential stabilization in switched stochastic dynamical networks, Nonlinearity 22, 889-911 (2009) · Zbl 1158.93413 · doi:10.1088/0951-7715/22/4/011
[7] Lu, J. Q.; Cao, J. D.: Adaptive synchronization in tree-like dynamical networks, Nonlinear analysis: real world applications 8, No. 4, 1252-1260 (2007) · Zbl 1125.34031 · doi:10.1016/j.nonrwa.2006.07.010
[8] Lu, J. Q.; Ho, D. W. C.; Kurths, J.: Consensus over directed static networks with arbitrary communication delays, Physical review E 80, No. 6, 066121 (2009)
[9] Wu, C. W.: Synchronization in coupled chaotic circuits and systems, (2002) · Zbl 1007.34044
[10] Lü, J. H.; Chen, G. R.: A time-varying complex dynamical network model and its controlled synchronization criteria, IEEE transactions on automatic control 50, No. 6, 841-846 (2005)
[11] Lu, J. Q.; Ho, D. W. C.; Wang, Z. D.: Pinning stabilization of linearly coupled stochastic neural networks via minimum number of controllers, IEEE transactions on neural networks 20, 1617-1629 (2009)
[12] Wang, X. F.; Chen, G. R.: Pinning control of scale-free dynamical networks, Physica A 310, No. 3--4, 521-531 (2002) · Zbl 0995.90008 · doi:10.1016/S0378-4371(02)00772-0
[13] Li, X.; Wang, X. F.; Chen, G. R.: Pinning a complex dynamical network to its equilibrium, IEEE transactions on circuits and systems I 51, No. 10, 2074-2087 (2004)
[14] Sorrentino, F.; Di Bernardo, M.; Garofalo, F.; Chen, G. R.: Controllability of complex networks via pinning, Physical review E 75, No. 4, 046103 (2007)
[15] Shi, H.; Wang, L.; Chu, T.: Virtual leader approach to coordinated control of multiple mobile agents with asymmetric interactions, Physica D 213, No. 1, 51-65 (2006) · Zbl 1131.93354 · doi:10.1016/j.physd.2005.10.012
[16] Cao, J.; Wang, Z.; Sun, Y.: Synchronization in an array of linearly stochastically coupled networks with time delays, Physica A 385, No. 2, 718-728 (2007)
[17] G.A. de Castro, F. Paganini, Convex synthesis of controllers for consensus, in: Proceedings of the American Control Conference, 2004, pp. 4933--4938.
[18] Doyle, J. C.; Glover, K. K.; Khargonekar, P.; Francis, B. A.: State-space solutions to standard H2 and H$\infty $ control problems, IEEE transactions on automatic control 34, 831-847 (1989) · Zbl 0698.93031 · doi:10.1109/9.29425
[19] Xu, S. Y.; Chen, T. W.: Robust H$\infty $ control for uncertain stochastic systems with state delay, IEEE transactions on automatic control 47, No. 12, 2089-2094 (2002)
[20] Wang, Z.; Yang, F.; Ho, D. W. C.; Liu, X.: Robust H$\infty $ filtering for stochastic time-delay systems with missing measurements, IEEE transactions on signal processing 54, No. 7, 2579-2587 (2006)
[21] Wang, Z.; Yang, F.; Ho, D. W. C.; Liu, X.: Robust H$\infty $ control for networked systems with random packet losses, IEEE transactions on systems, man, and cybernetics, part B 37, No. 4, 916-924 (2007)
[22] Yue, D.; Han, Q. L.; Lam, J.: Network-based robust H$\infty $ control of systems with uncertainty, Automatica 41, No. 6, 999-1007 (2005) · Zbl 1091.93007 · doi:10.1016/j.automatica.2004.12.011
[23] Arenas, A.; Díaz-Guilera, A.; Kurths, J.; Moreno, Y.; Zhou, C. S.: Synchronization in complex networks, Physics reports 469, No. 3, 93-153 (2008)
[24] Lu, W.; Chen, T.: New approach to synchronization analysis of linearly coupled ordinary differential systems, Physica D 213, No. 2, 214-230 (2006) · Zbl 1105.34031 · doi:10.1016/j.physd.2005.11.009
[25] Li, C. G.; Chen, G. R.: Synchronization in general complex dynamical networks with coupling delays, Physica A 343, 263-278 (2004)
[26] Gao, H. J.; Lam, J.; Chen, G. R.: New criteria for synchronization stability of general complex dynamical networks with coupling delays, Physics letters A 360, No. 2, 263-273 (2006) · Zbl 1236.34069
[27] Zhou, K. M.; Doyle, J. C.: Essentials of robust control, (1998) · Zbl 0890.93003
[28] Taussky, O.: A recurring theorem on determinants, The American mathematical monthly 56, No. 10, 672-676 (1949) · Zbl 0036.01301 · doi:10.2307/2305561
[29] Horn, R. A.; Johnson, C. R.: Matrix analysis, (1990) · Zbl 0704.15002
[30] Boyd, S. P.; Ghaoui, L. E. I.; Feron, E.; Balakrishnana, U.: Linear matrix inequalities in system and control theory, (1994) · Zbl 0816.93004
[31] Cao, J.; Li, P.; Wang, W.: Global synchronization in arrays of delayed neural networks with constant and delayed coupling, Physics letters A 353, No. 4, 318-325 (2006)
[32] Zou, F.; Nossek, J. A.: Bifurcation and chaos in cellular neural networks, IEEE transactions on circuits and systems I 40, No. 3, 166-173 (1993) · Zbl 0782.92003 · doi:10.1109/81.222797