This paper is concerned with the structural balance problem for complex dynamical network with the help of coupling effect related to the external stimulations. Consider a network with time-varying and value-weighted links, which can be regarded as a dynamic system. The link dynamic system is modeled as a Riccati matrix difference equation with the coupling matrix related to the external stimulations. By using the Kronecker product as an effective tool, a linear matrix inequality (LMI) approach is developed to derive a simple criterion for ensuring that the discrete link system asymptotically achieves structural balance, meanwhile, the external stimulations track a corresponding vector signal as well. Simulation examples are given to demonstrate the usefulness of the proposed control scheme in this paper.

中文翻译：

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通过确定的外部刺激对离散时变链接系统进行结构平衡的渐近跟踪控制

本文研究了借助与外部刺激相关的耦合效应的复杂动力网络的结构平衡问题。考虑一个具有时变和价值加权链接的网络，可以将其视为一个动态系统。链接动态系统被建模为与外部刺激相关的耦合矩阵的 Riccati 矩阵差分方程。通过使用克罗内克积作为有效工具，开发了一种线性矩阵不等式（LMI）方法，以推导一个简单的标准，以确保离散链接系统渐近地实现结构平衡，同时外部刺激也跟踪相应的矢量信号。仿真例子证明了本文提出的控制方案的有效性。