A Unifying Framework for Strong Structural Controllability

Jiajia Jia, Henk J. Van Waarde, Harry L. Trentelman, M. Kanat Camlibel*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

26 Citations (Scopus)
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This article deals with strong structural controllability of linear systems. In contrast to the existing work, the structured systems studied in this article have a so-called zero/nonzero/arbitrary structure, which means that some of the entries are equal to zero, some of the entries are arbitrary but nonzero, and the remaining entries are arbitrary (zero or nonzero). We formalize this in terms of pattern matrices, whose entries are either fixed zero, arbitrary nonzero, or arbitrary. We establish necessary and sufficient algebraic conditions for strong structural controllability in terms of full rank tests of certain pattern matrices. We also give a necessary and sufficient graph-theoretic condition for the full rank property of a given pattern matrix. This graph-theoretic condition makes use of a new color change rule that is introduced in this article. Based on these two results, we then establish a necessary and sufficient graph-theoretic condition for strong structural controllability. Moreover, we relate our results to those that exist in the literature and explain how our results generalize previous work.

Original languageEnglish
Article number9039736
Pages (from-to)391-398
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number1
Publication statusPublished - Jan-2021


  • Network controllability
  • pattern matrices
  • strong structural controllability
  • structured system

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