Stability of dynamical networks with non-identical nodes: A multiple v-Lyapunov function method
Stability of dynamical networks with non-identical nodes: A multiple v-Lyapunov function method
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DOI：
10.1016/j.automatica.2011.09.012
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发表时间：
2011-12
期刊：
影响因子：
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通讯作者：
Jun Zhao;D. Hill;Tao Liu
中科院分区：
文献类型：
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作者：
Jun Zhao;D. Hill;Tao Liu
通过引入多个V-Lyapunov函数，研究了具有不同节点的一般动力网络的全局渐近稳定性。在这样的网络中，耦合强度、内耦合矩阵和外耦合矩阵都是状态相关的、非线性的。利用矩阵范数和一些低维矩阵的特征值，给出了一个稳定性判据。基于这个准则，形成了一个最优化问题，其解可以用来检验全局渐近稳定性。我们还研究了如何在多V-Lyapunov函数方案下通过设计控制器来实现全局渐近稳定的问题。将控制行为视为外部耦合拓扑的重塑，并设计了相应的控制器。具体地，提出了一种添加或移除一定数量的链接的方法。文中还给出了耦合非恒等式Lorenz系统的稳定性分析和设计实例。
Global asymptotic stability of general dynamical networks with non-identical nodes is studied by introducing multiple V-Lyapunov functions. In such a network, the coupling strength, inner coupling matrix and outer coupling matrix are all allowed to be state-dependent and nonlinear. A stability criterion is proposed in terms of matrix norms and eigenvalues of some lower-dimensional matrices. Based on this criterion, an optimization problem is formed whose solution can be used to test global asymptotic stability. We also study the problem of how to achieve global asymptotic stability by design of controllers under the scheme of multiple V-Lyapunov functions. The control action is regarded as a re-shape of outer coupling topology and the associated controllers are designed. In particular, a method of adding or removing a certain number of links is proposed. Stability analysis of coupled non-identical Lorenz systems and a design example are also given to illustrate the proposed method.