Data-Driven Tests for Controllability

Vikas Kumar Mishra, Ivan Markovsky, Benjamin Grossmann

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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 paper, 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
Early online dateJun 2020
Publication statusPublished - Apr 2021


  • Behavioral approach
  • data-driven controllability
  • system identification

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