13
Bounds (proof)
q
Proof:
Consider
q
where (
A,B
) is controllable and (
C,A
) is observable.
q
q
q
Integration from
t= -
¥
to
t = 0
with
x(-
¥
)=0
and
x(0) = x
0
gives
•
•
•
Given
x(0) = x
0
and
w
= 0 for
t
³
0, the norm of
z(t)=Ce
At
x
0
can be
found from