Pinning impulsive control algorithms for complex network.
In this paper, we further investigate the synchronization of complex dynamical network via pinning control in which a selection of nodes are controlled at discrete times. Different from most existing work, the pinning control algorithms utilize only the impulsive signals at discrete time instants, which may greatly improve the communication channel efficiency and reduce control cost. Two classes of algorithms are designed, one for strongly connected complex network and another for non-strongly connected complex network. It is suggested that in the strongly connected network with suitable coupling strength, a single controller at any one of the network's nodes can always pin the network to its homogeneous solution. In the non-strongly connected case, the location and minimum number of nodes needed to pin the network are determined by the Frobenius normal form of the coupling matrix. In addition, the coupling matrix is not necessarily symmetric or irreducible. Illustrative examples are then given to validate the proposed pinning impulsive control algorithms.
School of Information and Mathematics, Yangtze University, Jingzhou 434023, People's Republic of China.
Wen
W
Sun
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People's Republic of China.
Jinhu
J
Lü
College of Mathematics and Statistics, Wuhan University, Wuhan 430072, People's Republic of China.
Shihua
S
Chen
School of Electrical and Computer Engineering, RMIT University, Melbourne VIC 3001, Australia.
Xinghuo
X
Yu