On the zeros of consensus networks

Author

Briegel, Benjamin ; Zelazo, Daniel ; Bürger, Mathias ; Allgöwer, Frank

Author_Institution

Inst. for Syst. Theor. & Autom. Control, Univ. of Stuttgart, Stuttgart, Germany

fYear

2011

fDate

12-15 Dec. 2011

Firstpage

1890

Lastpage

1895

Abstract

In this paper, we focus on the signal transfer between any two agents in a consensus network and provide an analysis of the resulting transfer function and transmission zeros. Our contributions include relating the distance between the input and output node to the relative degree of the system and showing that the gain factor of the transfer function is equal to the number of shortest paths between the two nodes. We show that for certain input-output configurations, the zeros interlace with the poles. Bounds on the zero locations and minimum phase properties of certain graph and input-output configurations are provided.

Keywords

graph theory; multi-agent systems; multi-robot systems; network theory (graphs); transfer functions; consensus network; graph; input-output configuration; poles; signal transfer; transfer function; transmission zeros; Eigenvalues and eigenfunctions; Filtering theory; Laplace equations; Polynomials; Symmetric matrices; Transfer functions; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on

Conference_Location

Orlando, FL

ISSN

0743-1546

Print_ISBN

978-1-61284-800-6

Electronic_ISBN

0743-1546

Type

conf

DOI

10.1109/CDC.2011.6161047

Filename

6161047