Image Processing Reference
In-Depth Information
5.4
Consider the system de
ned by
x
(
k
þ
1
) ¼
0
:
9x
(
k
) þ
u
(
k
)
Find the state feedback control law u
(
k
) ¼
K
(
k
)
x
(
k
)
minimizing the perform-
ance index
2
P
9
k
¼
0
[
x
2
2x
2
J
¼
(
10
) þ
1
(
k
) þ
0
:
5u
2
(
k
)]
5.5
Consider the system de
ned by
x
1
(
k
)
x
2
(
k
)
u
(
k
)
x
1
(
k
þ
1
)
0
61
00
:
1
0
¼
þ
x
2
(
k
þ
1
)
:
5
Find the state feedback control law u
(
k
) ¼
Kx
(
k
)
minimizing the performance
index
2
1
1
k
¼
0
x
1
(
k
) þ
2x
2
(
k
) þ
u
2
J
¼
(
k
)
5.6
Consider the system de
ned by
x
1
(
k
)
x
2
(
k
)
u
(
k
)
x
1
(
k
þ
)
1
01
0
1
1
¼
þ
x
2
(
k
þ
)
:
:
1
40
5
y
(
k
) ¼
x
1
(
k
)
Design a full-order state observer. The desired eigenvalues for the observer
matrix are
l
1
¼
0
:
1
and l
2
¼
0
:
2
5.7
Consider the system de
ned by
x
(
k
þ
1
) ¼
Ax
(
k
) þ
Bu
(
k
)
where
2
4
3
5
, B
¼
2
4
3
5
0
1
0
0
0
1
A
¼
0
0
1
0
:
10
:
25
0
:
4
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