12
Bounds of Function Norms
q
Suppose
is a balanced realization: that is, there
exists
q
S
=
diag
(
s
1
I
s
1
,
s
2
I
s
2
,…,
s
N
I
s
N
)
with
s
1
>
s
2
>
…
>
s
N
³
0,
q
such that
q
A
S
+
S
A*+BB*=0,
A*
S
+
S
A+C*C
=
0
•
Then
•
•
where
g(t)=Ce
At
B
.