Controllability: PBH test
PBH (Popov-Belevitch-Hautus) test:
•
The matrix [
A-
l
I, B
] has full row rank for all
l
in
C.
•
Let
l
and
x
be any eigenvalue and any corresponding
left eigenvector of
A
, i.e.,
x
*
A=
l
x
*
,
then
x
*
B
¹
0
.