Graph-Theoretic Analysis and Synthesis of Relative Sensing Networks

This work provides a general framework for the analysis and synthesis of a class of relative sensing networks (RSNs) in the context of its
H
₂
and
H
_∞
performance. We consider RSNs with homogeneous and heterogeneous agent dynamics. In both cases, explicit graph theoretic expressions and bounds for the
H
₂
and
H
_∞
performance are derived. The
H
₂
performance turns out to be a function of the number of edges in the graph, whereas the
H
_∞
performance is structure dependent and related to the spectral radius of the graph Laplacian. The analysis results are then used to develop synthesis methods for RSNs. An optimal topology is designed using the Kruskal's Algorithm for
H
₂
performance, and a semi-definite program for the
H
_∞
performance of uncertain RSNs.