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)
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China
Abstract This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances. A dynamical network is said to be robust to disturbance, if the $H_{\infty}$ norm of its transfer function matrix from the disturbance to the performance variable is satisfactorily small. It is shown that the disturbance rejection problem of a dynamical network can be solved by analysing the $H_{\infty}$ control problem of a set of independent systems whose dimensions are equal to that of a single node. A counter-intuitive result is that the disturbance rejection level of the whole network with a diffusive coupling will never be better than that of an isolated node. To improve this, local feedback injections are applied to a small fraction of the nodes in the network. Some criteria for possible performance improvement are derived in terms of linear matrix inequalities. It is further demonstrated via a simulation example that one can indeed improve the disturbance rejection level of the network by pinning the nodes with higher degrees than pinning those with lower degrees.
Received: 03 March 2009
Revised: 08 June 2009
Accepted manuscript online:
Fund: Project supported by the National
Natural Science Foundation of China (Grant No 10832006) and the Key
Projects of Educational Ministry of China (Grant No 107110).
Cite this article:
Li Zhong-Kui(李忠奎), Duan Zhi-Sheng(段志生), and Chen Guan-Rong(陈关荣) Disturbance rejection and $H_{\infty}$ pinning control of linear complex dynamical networks 2009 Chin. Phys. B 18 5228
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