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 H₂ and H_∞ performance. We consider RSNs with homogeneous and heterogeneous agent dynamics. In both cases, explicit graph theoretic expressions and bounds for the H₂ and H_∞ performance are derived. The H₂ 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 H₂ performance, and a semi-definite program for the H_∞ performance of uncertain RSNs.