Algebraic characterization of observability in distance-regular consensus networks

Abstract

Abstract-In this paper, we study the observability issue in consensus networks modeled with strongly regular graphs or distance regular graphs. We derive a Kalman-like simple algebraic criterion for observability in distance regular graphs. This criterion consists in evaluating the rank of a matrix built with the components of the Bose-Mesner algebra associated with the considered graph. Then, we state a simple necessary condition of observability based on parameters of the graph, namely the diameter, the degree, and the number of vertices of the graph.

Observability in Connected Strongly Regular Graphs and Distance Regular Graphs

“…Therefore, our study concerns neighborhood observability and global-observability. We first extend the preliminary results on the algebraic characterization reported in [8] and then introduce new results related to a graph characterization of observability, which does not require the computation of a matrix rank. Precisely, we show how building a bipartite graph that captures the observability properties of the graph.…”

“…The matrices C n A l , l = 0, 1, • • • , D, involved inÔ n have also some nice properties. For instance the following result demonstrated in [8] will be particularly useful in the sequel.…”

“…• neighborhood observable from a given node if that node can reconstruct the entire network state from its own measurements and those of its neighbors. This issue was studied in [8].…”

Observability of leader‐based discrete‐time multi‐agent systems with switching topology

“…Another parallel study is based on algebraic features of controllability and observability for MASs in [29–36], for example, applied for Laplacian spectrum estimation [29], distance‐regular consensus networks [30], distributed sensor networks [4–6, 34] and so on. In particular, some recent works discussed the observability, boundedness, detectability and stability for sensor networks with or without switching topology based on Kalman consensus filtering problems in [4–6], respectively, in which the models and research techniques are different from MASs, although they are both based on consensus protocols.…”

On the Observability of Leader‐Based Multiagent Systems with Fixed Topology

“…In [25], the authors established a decentralized condition for controllability and observability of networked MASs using decentralized Laplacian spectrum estimation. e observability of a network system was investigated based on average consensus algorithm for path and cycle graphs in [26], graph Cartesian products in [27], regular graphs and distance-regular graphs [28,29], and equitable partition [30], respectively. Furthermore, the observability of switched linear systems and switched multiagent systems was studied in [31,32], respectively.…”