On the structural target controllability of undirected networks

Jingqi Li, Ximing Chen, Sergio Pequito, George J. Pappas, Victor M. Preciado

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
15 Downloads (Pure)


In this article, we study the target controllability problem of networked dynamical systems,in which we are tasked to steer a subset of network nodes toward a desired objective. More specifically, we derive necessary and sufficient conditions for the structural target controllability of linear time-invariant (LTI) systems with symmetric state matrices, such as those representing undirected dynamical networks with unknown link weights. To achieve our goal, we first characterize the generic rank of symmetrically structured matrices, as well as the modes of any numerical realization. Subsequently, we provide graph-theoretic necessary and sufficient conditions for the structural target controllability of undirected networks with multiple control nodes. In addition, we show that these results can be extended and lead to a necessary and sufficient condition of the structural output controllability. However, different from structural target controllability, we prove that verifying the proposed conditions on structural output controllability in undirected networks is NP-hard.

Original languageEnglish
Pages (from-to)4836-4843
JournalIEEE Transactions on Automatic Control
Issue number10
Publication statusPublished - 2021

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Computational complexity
  • Controllability
  • Dynamical systems
  • Graph theory
  • Linear systems
  • networked control systems
  • structured linear systems
  • Symmetric matrices
  • Target controllability
  • Tools


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