Detectability of distributed consensus-based observer networks: An elementary analysis and extensions

TL;DR

This paper analyzes the detectability conditions of distributed observer networks, providing a graph-topology-based proof and extending previous results to include nonidentical interconnection matrices.

Contribution

It offers an elementary, topology-based proof of a key eigenvalue multiplicity result and extends detectability conditions to networks with nonidentical interconnection matrices.

Findings

Graph topology analysis links eigenvalue multiplicity to network structure.

Detectability of the network relates to local detectability and observability of nodes.

Extension to nonidentical matrices broadens applicability of the results.

Abstract

This paper continues the study of local detectability and observability requirements on components of distributed observers networks to ensure detectability properties of the network. First, we present a sketch of an elementary proof of the known result equating the multiplicity of the zero eigenvalue of the Laplace matrix of a digraph to the number of its maximal reachable subgraphs. Unlike the existing algebraic proof, we use a direct analysis of the graph topology. This result is then used in the second part of the paper to extend our previous results which connect the detectability of an observer network with corresponding local detectability and observability properties of its node observers. The proposed extension allows for nonidentical matrices to be used in the interconnections.