Detectability of distributed consensus-based observer networks: An elementary analysis and extensions
For researchers in distributed control and estimation, this work offers a simpler proof and a modest extension of existing detectability conditions for observer networks.
This paper provides an elementary graph-theoretic proof of the relationship between the zero eigenvalue multiplicity of a Laplacian matrix and the number of maximal reachable subgraphs, and extends previous results on distributed observer network detectability to allow nonidentical interconnection matrices.
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.