H2 norm accumulation and its impact on synchronisation of complex dynamical networks
H2 norm accumulation and its impact on synchronisation of complex dynamical networks
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DOI：
10.1080/00207170903062182
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发表时间：
2009-10
影响因子：
2.1
通讯作者：
Z. Duan;Jinzhi Wang;Guanrong Chen;Lin Huang
中科院分区：
文献类型：
--
作者：
Z. Duan;Jinzhi Wang;Guanrong Chen;Lin Huang
本文研究线性耦合动态网络的H 2范数积累问题。构建了一个有趣的外耦合关系，在这种关系下，新构建的列输入行输出矩阵网络的h2范数随节点数N呈指数级快速增长：当N较大时，其增长速度一般远快于2n，而每个节点的h2范数为1。而扩散耦合网络的H 2范数等于γ2 N，即在网络稳定时仅线性增加，其中γ2为单个节点的H 2范数。具有反对称耦合的网络的h2范数也随着节点数n的增加而增加，但速度很慢。其他具有块对角线输入和块对角线输出矩阵的网络表现类似。结果表明，尽管网络结构是线性的，但不同网络中h2范数的变化非常复杂。最后，讨论了局部线性化网络的h2范数对具有Lur'e节点动态的网络输出的影响，证明了h2范数对网络输出同步行为的显著影响。
This article addresses the H 2 norm accumulation problem of linearly coupled dynamical networks. An interesting outer-coupling relationship is constructed, under which the H 2 norm of the newly constructed network with column-input and row-output matrices increases exponentially fast in terms of the node number N: it increases generally much faster than 2 N when N is large while the H 2 norm of each node is 1. However, the H 2 norm of the network with a diffusive coupling is equal to γ2 N, i.e. increasing only linearly, when the network is stable, where γ2 is the H 2 norm of a single node. And the H 2 norm of the network with antisymmetrical coupling also increases, but rather slowly, with respect to the node number N. Other networks with block-diagonal-input and block-diagonal-output matrices behave similarly. It demonstrates that the changes of H 2 norms in different networks are very complicated, despite the fact that the network structures are linear. Finally, the influence of the H 2 norm of the locally linearised network on the output of a network with Lur'e node dynamics is discussed, demonstrating a significant effect of the H 2 norm on the network output synchronisation behaviours.