H2 performance of agreement protocol with noise: An edge based approach

This work presents an H₂ performance analysis of the agreement protocol in the presence of noise. The agreement protocol is first transformed into an equivalent system induced by the dynamics of the relative, or edge, system states. The edge based representation is used to perform an H₂ analysis of the system highlighting the roles of cycles in this context. For spanning trees and and certain k-regular graphs, a characterization of the H₂ norm is given in terms of properties of the graph. These results are used to formulate a semi-definite program for sensor selection and placement. Each sensor has an associated cost and fidelity and the developed SDP determines which sensors to use and where to place them such that the H₂ norm of the system, in addition to the sensor costs, are minimized.