Detectability
The following are equivalent:
•
(
C,A
) is detectable.
•
A+LC
is stable for a suitable L.
•
(
A
*
,C
*
) is controllable.
PBH test:
•
The matrix
has full column rank for all
Re
l
³
0.
•
For all
l
and
y
such that
Ay=
l
y
,
Re
l
³
0,
and
Cy
¹
0.