The main result Hautus lemma

1 main result

1.1 hautus lemma controllability
1.2 hautus lemma stabilizability
1.3 hautus lemma observability
1.4 hautus lemma detectability

the main result

there exist multiple forms of lemma.

hautus lemma controllability

the hautus lemma controllability says given square matrix




a

∈

m

n


(
ℜ
)


{\displaystyle \mathbf {a} \in m_{n}(\re )}

,




b

∈

m

n
×
m


(
ℜ
)


{\displaystyle \mathbf {b} \in m_{n\times m}(\re )}

following equivalent:

hautus lemma stabilizability

the hautus lemma stabilizability says given square matrix




a

∈

m

n


(
ℜ
)


{\displaystyle \mathbf {a} \in m_{n}(\re )}

,




b

∈

m

n
×
m


(
ℜ
)


{\displaystyle \mathbf {b} \in m_{n\times m}(\re )}

following equivalent:

hautus lemma observability
hautus lemma detectability

the hautus lemma detectability says given square matrix




a

∈

m

n


(
ℜ
)


{\displaystyle \mathbf {a} \in m_{n}(\re )}

,




c

∈

m

m
×
n


(
ℜ
)


{\displaystyle \mathbf {c} \in m_{m\times n}(\re )}

following equivalent: