Algebraic Characterization of Observability in Distance-Regular Consensus Networks

Alain Y. Kibangou 1 Christian Commault 2
1 NECS - Networked Controlled Systems
Inria Grenoble - Rhône-Alpes, GIPSA-DA - Département Automatique
2 GIPSA-SLR - SLR
GIPSA-DA - Département Automatique
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.
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Alain Y. Kibangou, Christian Commault. Algebraic Characterization of Observability in Distance-Regular Consensus Networks. 52nd IEEE Conference on Decision and Control (CDC 2013), Dec 2013, Florence, Italy. pp.n/c. ⟨hal-00913926⟩

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