Computing L
2
and H
2
Norms
§
Let
G
(
s
)
Î
L
2
and
g
(
t
) =
L
-1
[
G
(
s
)]. Then
•
•
•
•
•
Consider
G(s)=C(sI-A)
-1
B
Î
RH
2
. Then we have
•
||
G
(
s
)||
2
2
= trace(
B*L
0
B
) = trace(
CL
c
C*
)
•
where
L
0
and
L
c
are observability and controllability Gramians:
•
AL
c
+L
c
A*+BB*
= 0
A*L
0
+L
0
A+C*C
= 0.