2011/09/16 by Gianfranco Parlangeli, Giuseppe Notarstefano, Parlangeli, Gianfranco +1
Biochemistry, Genetics and Molecular Biology · Computer Science · #Distributed Control Multi-Agent Systems #FOS: Electrical engineering #FOS: Mathematics #Gene Regulatory Network Analysis #Neural Networks Stability and Synchronization #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1109.3556
openalex publication_date 2011/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we investigate the reachability and observability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a path or a cycle. More in detail, we provide necessary and sufficient conditions, based on simple algebraic rules from number theory, to characterize all and only the nodes from which the network system is reachable (respectively observable). Interesting immediate corollaries of our results are: (i) a path graph is reachable (observable) from any single node if and only if the number of nodes of the graph is a power of two, n=2i, i∈ \natural, and (ii) a cycle is reachable (observable) from any pair of nodes if and only if n is a prime number. For any set of control (observation) nodes, we provide a closed form expression for the (unreachable) unobservable eigenvalues and for the eigenvectors of the (unreachable) unobservable subsystem.