Robust H∞ observer-based control for synchronization of a class of complex dynamical networks

doi:10.1088/1674-1056/20/6/060504

Abstract This paper is concerned with the robust H_∞ synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each node and to improve the H_∞ performance related to the synchronization error and observation error despite the external disturbance. Based on the Lyapunov stability theory, a synchronization criterion is obtained under which the controlled network can be robustly stabilized onto a desired state with a guaranteed H_∞ performance. The controller and the observer gains can be given by the feasible solutions of a set of linear matrix inequalities (LMIs). The effectiveness of the proposed control scheme is demonstrated by a numerical example through simulation.

Keywords: complex dynamical network robust H_∞ synchronization Lur'e system decentralized observer

Received: 02 November 2010
Revised: 07 January 2011
Accepted manuscript online:

PACS:

05.45.Xt

(Synchronization; coupled oscillators)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 60274099) and the National High Technology Research and Development Program of China (Grant No. 2004AA412030).

Cite this article:

Zheng Hai-Qing(郑海青) and Jing Yuan-Wei(井元伟) Robust H_∞ observer-based control for synchronization of a class of complex dynamical networks 2011 Chin. Phys. B 20 060504

[1]	Albert R and Barabasi A L 2002 Rev. Mod. Phys. 74 47
[2]	Dorogovtsev S N and Mendes J F F 2002 Adv. Phys. 51 1079.
[3]	Chen G, Zhou J and Liu Z 2004 Int. J. Bifur. Chaos 14 2229.
[4]	Wu J S and Jiao L C 2007 Physcia A 386 513.
[5]	Xiang J and Chen G R 2007 Automatica 43 1049.
[6]	Zhang R, Hu M F and Xu Z Y 2007 Phys. Lett. A 368 276.
[7]	Xiao Y Z, Xu W, Li X C and Tang S F 2008 Chin. Phys. B 17 80
[8]	Lu J Q and Ho D W C 2008 Chaos, Solitons and Fractals 37 1497
[9]	Tu L L and Lu J A 2009 Comput. Math. Appl. 57 28
[10]	Perales G S, Velazquez E R and Rodriguez D V 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 2528
[11]	Li R, Duan Z S and Chen G R 2009 Chin. Phys. B 18 106
[12]	Zhou J, Lu J A and Lü J H 2008 Automatica 44 996
[13]	Wang L, Dai H P, Dong H, Shen Y H and Sun Y X 2008 Phys. Lett. A 372 3632
[14]	Zhang Q Z and Li Z K 2009 Chin. Phys. B 18 2176
[15]	Gu D W and Poon F W 2001 IEEE Trans. Automat. Control 46 1958
[16]	Chen J D, Yang C D, Lien C H and Horng J H 2008 Inform. Sci. 178 4699
[17]	Dhbaibi S, Tlili A S, Elloumi S and Braiek N B 2009 ISA Transactions 48 458
[18]	Tsuneda A 2005 Int. J. Bifur. Chaos 15 1
[19]	Ruoff P, Vinsjevik M, Monnerjahnsjevik C and Rensing L 2001 J. Theor. Biol. 209 29
[20]	Gazi V and Passino K M 2004 Int. J. Control 77 1567
[21]	Yalccin M E, Suykens J A K and Vandewalle J 2001 Int. J. Bifur. Chaos 11 1707
[22]	Souza F O, Palhares R M, Mendes E M A and Tôrres L A B 2008 Int. J. Bifur. Chaos 18 187
[23]	Huang H and Feng G 2008 Chaos 18 033113
[24]	Liu X, Wang J Z and Huang L 2007 Physica A 383 733
[25]	Liu X, Wang J Z and Huang L 2007 Physica A 386 543
[26]	Xu S Y and Yang Y 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 3230
[27]	Castillo C P, Hernandez C C and Gutierrez R M L 2009 Chaos, Solitons and Fractals 40 1963
[28]	Wu C W 2002 Synchronization in Coupled Chaotic Circuits and Systems (Singapore: World Scientific)

[1]	Hash function construction using weighted complex dynamical networks Song Yu-Rong (宋玉蓉), Jiang Guo-Ping (蒋国平). Chin. Phys. B, 2013, 22(4): 040506.
[2]	Topology identification for a class of complex dynamical networks using output variables Fan Chun-Xia(樊春霞), Wan You-Hong(万佑红), and Jiang Guo-Ping(蒋国平) . Chin. Phys. B, 2012, 21(2): 020510.
[3]	Impulsive synchronization of two coupled complex networks with time-delayed dynamical nodes Wang Shu-Guo(王树国) and Yao Hong-Xing(姚洪兴) . Chin. Phys. B, 2011, 20(9): 090513.
[4]	Fault diagnosis of time-delay complex dynamical networks using output signals Liu Hao (刘昊), Song Yu-Rong (宋玉蓉), Fan Chun-Xia (樊春霞), Jiang Guo-Ping (蒋国平). Chin. Phys. B, 2010, 19(7): 070508.
[5]	Pinning control of complex Lur'e networks Zhang Qing-Zhen(张庆振) and Li Zhong-Kui(李忠奎). Chin. Phys. B, 2009, 18(6): 2176-2183.
[6]	Disturbance rejection and $H_{\infty}$ pinning control of linear complex dynamical networks Li Zhong-Kui(李忠奎), Duan Zhi-Sheng(段志生), and Chen Guan-Rong(陈关荣) . Chin. Phys. B, 2009, 18(12): 5228-5234.
[7]	Cost and effect of pinning control for network synchronization Li Rong(李嵘), Duan Zhi-Sheng(段志生), and Chen Guan-Rong(陈关荣). Chin. Phys. B, 2009, 18(1): 106-118.
[8]	Synchronization of stochastically hybrid coupled neural networks with coupling discrete and distributed time-varying delays Tang Yang (唐漾), Zhong Hui-Huang(钟恢凰), Fang Jian-An(方建安). Chin. Phys. B, 2008, 17(11): 4080-4090.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Robust H_∞ observer-based control for synchronization of a class of complex dynamical networks

Cite this article:

Online attention