Tradeoff between Controllability and Robustness in Diffusively Coupled Networks

Waseem Abbas, Mudassir Shabbir, A. Yasin Yazicioglu, Aqsa Akber

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In this article, we demonstrate a conflicting relationship between two crucial properties - controllability and robustness - in linear dynamical networks of diffusively coupled agents. In particular, for any given number of nodes N and diameter D, we identify networks that are maximally robust using the notion of Kirchhoff's index and then analyze their strong structural controllability. For this, we compute the minimum number of leaders, which are the nodes directly receiving external control inputs, needed to make such networks controllable under all feasible coupling weights between agents. Then, for any N and D, we obtain a sharp upper bound on the minimum number of leaders needed to design strong structurally controllable networks with N nodes and D diameter. We also discuss that the bound is best possible for arbitrary N and D. Moreover, we construct a family of graphs for any N and D such that the graphs have maximal edge sets (maximal robustness) while being strong structurally controllable with the number of leaders in the proposed sharp bound. We then analyze the robustness of this graph family. The results suggest that optimizing robustness increases the number of leaders needed for strong structural controllability. Our analysis is based on graph-theoretic methods and can be applied to exploit network structure to co-optimize robustness and controllability in networks.

Original languageEnglish (US)
Article number9146993
Pages (from-to)1891-1902
Number of pages12
JournalIEEE Transactions on Control of Network Systems
Issue number4
StatePublished - Dec 2020

Bibliographical note

Publisher Copyright:
© 2014 IEEE.


  • Network controllability
  • network robustness
  • network structure


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