This study considers merging dynamical networks (relative sensing networks in this paper) in terms of a stability margin criterion. The main motivation of this consideration is that merging can cause a significant drop in the stability margin of merged network with respect to the original networks initially with ample stability margins. In this paper, various types of network merging (i.e. undirected/directed homogeneous/heterogeneous dynamical network merging via one-way/two-way links) are analysed to show their effects on the stability margin. In particular, it is shown that (1) merging with one-way links yields the stability margin less than the original networks’; (2) merging undirected homogeneous networks with two-way links results in a stability margin being at least a quantity solely characterized by the positive realness (PRness) of SISO (Single-Input-Single-Output) local dynamics; (3) the quantity depends both on the PRness of SISO local dynamics and the eigenvalues of Laplacian matrix, in case of merging directed homogeneous networks with two-way links; (4) two-way merging using multiple nodes may allow for a large increase in the stability margin; and (5) merging heterogeneous networks may be simply treated as merging homogeneous networks by exploiting the design of link dynamics. Several numerical results are presented to show their consistency with the performed analysis.

本研究考虑根据稳定裕度准则合并动态网络（本文中的相对传感网络）。这种考虑的主要动机是，合并可能会导致合并后的网络的稳定性裕度相对于最初具有足够稳定性裕度的原始网络显着下降。在本文中，分析了各种类型的网络合并（即通过单向/双向链接的无向/有向均质/异构动态网络合并），以显示它们对稳定性裕度的影响。特别是，它表明（1）与单向链路合并产生的稳定性裕度小于原始网络的稳定性裕度；（2）将具有双向链接的无向齐次网络合并会导致稳定裕度至少是一个仅以SISO（单输入单输出）局部动力学的正真实性（PRness）为特征的量；（3）在合并有双向链接的有向齐次网络的情况下，数量取决于SISO局部动力学的PRness和拉普拉斯矩阵的特征值。（4）使用多个节点的双向合并可能会大大增加稳定性裕度；（5）通过利用链路动态设计，可以将合并异构网络简单地视为合并异构网络。提出了几个数值结果，以显示它们与所进行的分析的一致性。（3）在合并有双向链接的有向齐次网络的情况下，数量取决于SISO局部动力学的PRness和拉普拉斯矩阵的特征值。（4）使用多个节点的双向合并可能会大大增加稳定性裕度；（5）通过利用链路动态设计，可以将合并异构网络简单地视为合并异构网络。提出了几个数值结果，以显示它们与所进行的分析的一致性。（3）在合并有双向链接的有向齐次网络的情况下，数量取决于SISO局部动力学的PRness和拉普拉斯矩阵的特征值。（4）使用多个节点的双向合并可能会大大增加稳定性裕度；（5）通过利用链路动态设计，可以将合并异构网络简单地视为合并异构网络。提出了几个数值结果，以显示它们与所进行的分析的一致性。