Graph Distances and Controllability of Networks

A. Y. Yazicioglu, Waseem Abbas, Magnus Egerstedt

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


In this technical note, we study the controllability of diffusively coupled networks from a graph theoretic perspective. We consider leader-follower networks, where the external control inputs are injected to only some of the agents, namely the leaders. Our main result relates the controllability of such systems to the graph distances between the agents. More specifically, we present a graph topological lower bound on the rank of the controllability matrix. This lower bound is tight, and it is applicable to systems with arbitrary network topologies, coupling weights, and number of leaders. An algorithm for computing the lower bound is also provided. Furthermore, as a prominent application, we present how the proposed bound can be utilized to select a minimal set of leaders for achieving controllability, even when the coupling weights are unknown.

Original languageEnglish (US)
Article number7439805
Pages (from-to)4125-4130
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number12
StatePublished - Dec 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.


  • Controllability
  • decentralized control
  • graph theory
  • multi-agent networks


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