Merging relative sensing networks: A stability margin perspective

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.