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Front. Inform. Technol. Electron. Eng.  2011, Vol. 12 Issue (6): 470-477    DOI: 10.1631/jzus.C1010247
    
Number estimation of controllers for pinning a complex dynamical network
Lei Wang*,1, Huan Shi2, You-xian Sun2
1 School of Mathematics and Systems Science and LMIB, Beihang University, Beijing 100191, China 2 State Key Lab of Industrial Control Technology, Institute of Industrial Process Control, Zhejiang University, Hangzhou 310027, China
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Abstract  Number estimation of controllers is a fundamental question in pinning synchronization of complex networks. This paper studies the problem of controller number in synchronizing a complex network of coupled dynamical systems by means of pinning. For a complex network with a symmetric coupling matrix and full coupling between the nodes, we formulate network synchronization via pinning as a linear matrix inequality criterion, and provide a lower bound and an upper bound of the controller number for a given complex network with fixed architecture. Several numerical examples with Barabási-Albert network topologies are provided to verify our theoretical results.

Key words： Pinning control      Number estimation      Synchronization      Complex networks     
Received: 28 May 2010      Published: 07 June 2011
CLC:  TP13  
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Lei Wang, Huan Shi, You-xian Sun. Number estimation of controllers for pinning a complex dynamical network. Front. Inform. Technol. Electron. Eng., 2011, 12(6): 470-477.

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http://www.zjujournals.com/xueshu/fitee/10.1631/jzus.C1010247     OR     http://www.zjujournals.com/xueshu/fitee/Y2011/V12/I6/470


Number estimation of controllers for pinning a complex dynamical network

Number estimation of controllers is a fundamental question in pinning synchronization of complex networks. This paper studies the problem of controller number in synchronizing a complex network of coupled dynamical systems by means of pinning. For a complex network with a symmetric coupling matrix and full coupling between the nodes, we formulate network synchronization via pinning as a linear matrix inequality criterion, and provide a lower bound and an upper bound of the controller number for a given complex network with fixed architecture. Several numerical examples with Barabási-Albert network topologies are provided to verify our theoretical results.

关键词： Pinning control,  Number estimation,  Synchronization,  Complex networks 
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