H∞ performance and robust topology design of relative sensing networks

This work provides a general framework for the analysis and synthesis of a class of relative sensing networks (RSN) in the context of its H_∞ performance. In an RSN, the underlying connection topology couples each agent at their outputs. A distinction is made between RSN with homogeneous agent dynamics and RSN with heterogeneous dynamics. In both cases, explicit graph theoretic expressions and bounds for the H_∞ performance are derived. 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. Using results from robust semi-definite programming, a synthesis procedure for the design of a robust sensing topology is derived.