Performance of first and second order linear networked systems over digraphs
Performance of first and second order linear networked systems over digraphs
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DOI：
10.1109/cdc.2017.8263893
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发表时间：
2017-12
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影响因子：
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通讯作者：
Hasan Giray Oral;Enrique Mallada;D. Gayme
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文献类型：
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作者：
Hasan Giray Oral;Enrique Mallada;D. Gayme
本文研究了具有全局可达节点的有向图上的线性网络动力系统的性能。我们考虑一阶和二阶系统的分布干扰，并定义了一个输出，量化的性能，通过输入输出H2范数的系统。我们开发了一个通用的框架，计算这类系统的H2范数，并应用此框架来评估两个性能指标的系统，其基础网络图的结果在正常的加权图拉普拉斯矩阵。我们发现封闭形式的解决方案的措施，量化的状态从平均值的总偏差，并量化相邻节点的状态之间的加权平方差的措施上的界限。数值算例表明，由于拉普拉斯算子的复特征值，连接在循环图上的二阶系统当其底层图是有向的时可能具有更好的性能。结果还表明，当网络规模足够大时，无论是线图还是完全图，对称系统的H2范数都小于或等于相应的扰动非对称系统的H2范数.
In this paper we investigate the performance of linear networked dynamical systems over digraphs with a globally reachable node. We consider first and second order systems subject to distributed disturbances and define an output that quantifies the performance through the input-output H2 norm of the system. We develop a generalized framework for computing the H2 norm for this class of systems, and apply this framework to evaluate two performance measures for systems whose underlying network graphs result in normal weighted graph Laplacian matrices. We find closed-form solutions for the measure that quantifies the total deviation of the states from the average, and bounds on the measure that quantifies the weighted squared difference between the states of neighboring nodes. Numerical examples indicate that a second order system connected over a cycle graph may have better performance when its underlying graph is directed due to complex eigenvalues of the Laplacian. The results also indicate that the H2 norm of a symmetric system is less than or equal to that of the corresponding perturbed non-symmetric system for either line or complete graphs when the network size is sufficiently large.