Data-Driven Tests for Controllability

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 the assumptions for is that underlying linear time-invariant controllable. In this letter, extended address uncontrollable systems. Then, a algebraic test derived check whether controllable or not. An algorithm based singular value decomposition Hankel matrix constructed from data provided implement developed test. has cubic computational cost. Examples are given illustrate theoretical results.