Before revision: Hautus Lemma for controllability The Hautus lemma for controllability says that given a square matrix and a the following are equivalent: The pair is controllable For all it holds that For all that are eigenvalues of it holds that Hautus Lemma for stabilizability The Hautus lemma for stabilizability says that given a square matrix and a the following are equivalent: The pair is stabilizable For all that are eigenvalues of and for which it holds that Hautus Lemma for observability The Hautus lemma for observability says that given a square matrix and a the following are equivalent: The pair is observable
After revision: .Hautus Lemma for controllability The Hautus lemma for controllability says that given a square matrix and a the following are equivalent: The pair is controllable For all it holds that For all that are eigenvalues of it holds that Hautus Lemma for stabilizability The Hautus lemma for stabilizability says that given a square matrix and a the following are equivalent: The pair is stabilizable For all that are eigenvalues of and for which it holds that Hautus Lemma for observability The Hautus lemma for observability says that given a square matrix and a the following are equivalent: The pair is observable