Stability analysis and decentralized control of a class of complex dynamical networks
Stability analysis and decentralized control of a class of complex dynamical networks
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一类复杂动态网络的稳定性分析与分散控制
DOI：
10.1016/j.automatica.2007.08.005
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发表时间：
2008-04-01
期刊：
影响因子：
6.4
通讯作者：
Huang, Lin
中科院分区：
文献类型：
--
作者：
Duan, Zhisheng;Wang, Jinzhi;Huang, Lin
本文研究了线性和扇形非线性复杂动态网络的稳定性分析和分散控制问题。给出了一种特殊分散控制策略下线性网络稳定和稳定的充分必要条件。重点研究了星形网络和全局耦合网络这两类线性规则网络。将动态网络看作是由若干子系统组成的大系统，在此基础上研究了网络的稳定性与其相应子系统的稳定性之间的关系。指出了这一点。在某些特殊情况下，为了保证整个网络的稳定，某些子系统必须是不稳定的。此外，还提出了一种基于参数相关李雅普诺夫函数的控制器设计方法。此外，还研究了互联Lur’e系统和Lur’e系统的对称网络。将一个Lur’e系统网络的绝对稳定性测试分为若干个独立的Lur’e系统的绝对稳定性测试。最后，给出了几个数值算例来说明理论结果。(c) 2007 Elsevier Ltd.版权所有。
In this paper, stability analysis and decentralized control problems are addressed for linear and sector-nonlinear complex dynamical networks. Necessary and sufficient conditions for stability and stabilizability under a special decentralized control strategy are given for linear networks. Especially, two types of linear regular networks, star-shaped networks and globally coupled networks, are studied in detail. A dynamical network is viewed as a large-scale system composing of some subsystems, based on which the relationship between the stability of a network and the stability of its corresponding subsystems is investigated. It is pointed out. that some subsystems must be unstable for the whole network to be stable in some special cases. Moreover, a controller design method based on a parameter-dependent Lyapunov function is provided. Furthermore, interconnected Lur'e systems and symmetrical networks of Lur'e systems are similarly studied. The test of absolute stability of a network of Lur'e systems is separated into the test of absolute stability of several independent Lur'e systems. Finally, several numerical examples are given to illustrate the theoretical results. (c) 2007 Elsevier Ltd. All rights reserved.