Hautus lemma

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In control theory and in particular when studying the controllability of a linear time-invariant system in state space form, the Hautus lemma, named after Malo Hautus, can prove to be a powerful tool. This result appeared first in [1] and.[2] Today it can be found in most textbooks on control theory.

The main result

The Hautus lemma says that given a square matrix and a the following are equivalent:

  1. The pair is controllable
  2. For all it holds that
  3. For all that are eigenvalues of it holds that

References

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