Data-Driven Tests for Controllability

Vikas Kumar Mishra, Ivan Markovsky, Ben Grossmann

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


The fundamental lemma due to Willems et al. 'A note on persistency of excitation,' Syst. Control Lett., vol. 54, no. 4, pp. 325-329, 2005 plays an important role in system identification and data-driven control. One of the assumptions for the fundamental lemma is that the underlying linear time-invariant system is controllable. In this letter, the fundamental lemma is extended to address system identification for uncontrollable systems. Then, a data-driven algebraic test is derived to check whether the underlying system is controllable or not. An algorithm based on the singular value decomposition of a Hankel matrix constructed from the data is provided to implement the developed test. The algorithm has cubic computational cost. Examples are given to illustrate the theoretical results.

Original languageEnglish
Article number9121339
Pages (from-to)517-522
Number of pages6
JournalIEEE Control Systems Letters
Issue number2
StatePublished - 1 Apr 2021
Externally publishedYes


  • Behavioral approach
  • data-driven controllability
  • system identification

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization


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