Stability and Stabilizability
A
is
stable
if
Re
l
(A)<0
.
•
(
A,B
) is stabilizable.
•
A+BF
is stable for some
F
.
PBH test:
•
The matrix [
A-
l
I, B
] has full row rank for all
Re
l
³
0
.
•
For all
l
and
x
such that
x
*
A
=x
*
l
and
Re
l
³
0, x
*
B
¹
0.