Robust Synchronization for 2-D Discrete-Time Coupled Dynamical Networks
Robust Synchronization for 2-D Discrete-Time Coupled Dynamical Networks
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DOI：
10.1109/tnnls.2012.2193414
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发表时间：
2012-04
影响因子：
10.4
通讯作者：
Jinling Liang;Zidong Wang;Xiaohui Liu;P. Louvieris
中科院分区：
文献类型：
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作者：
Jinling Liang;Zidong Wang;Xiaohui Liu;P. Louvieris
在本文中，解决了二维耦合动态网络阵列的新同步问题。所研究的系统类别由二维非线性状态空间模型描述，该模型源自著名的 Fornasini-Marchesini 第二模型。对于这样一个新的二维复杂网络模型，网络动力学和耦合都沿两个独立的方向演化。提出了一种新的同步概念来解释所有二维动态网络的传播在耦合强度的影响下在两个方向上同步的现象。解决问题的目的是首先导出确保全局同步的充分条件，然后将获得的结果扩展到更一般的情况，其中系统矩阵包含范数有界或多面参数不确定性。开发了类似能量的二次函数，并大量使用 Kronecker 产品，以建立易于验证的条件，在该条件下，所解决的二维复杂网络模型实现全局同步。最后，给出了一个数值例子来说明理论结果和所提出的同步方案的有效性。
In this paper, a new synchronization problem is addressed for an array of 2-D coupled dynamical networks. The class of systems under investigation is described by the 2-D nonlinear state space model which is oriented from the well-known Fornasini-Marchesini second model. For such a new 2-D complex network model, both the network dynamics and the couplings evolve in two independent directions. A new synchronization concept is put forward to account for the phenomenon that the propagations of all 2-D dynamical networks are synchronized in two directions with influence from the coupling strength. The purpose of the problem addressed is to first derive sufficient conditions ensuring the global synchronization and then extend the obtained results to more general cases where the system matrices contain either the norm-bounded or the polytopic parameter uncertainties. An energy-like quadratic function is developed, together with the intensive use of the Kronecker product, to establish the easy-to-verify conditions under which the addressed 2-D complex network model achieves global synchronization. Finally, a numerical example is given to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme.