Image Processing Reference
In-Depth Information
Equation 5.83 can be modi
ed as
2
3
2
3
1
C
CA
CA
2
.
CA
N
1
0
0
.
0
1
4
5
4
5
K
¼
P
(
A
)
(
5
:
84
)
The MATLAB pole-placement command can also be used to compute the observer
gain matrix as G
¼ place(
A
T
, B
T
, P
)
, and then K
¼
G
T
. The block diagram of the
full-order observer is shown in Figure 5.6. Note that the necessary and suf
cient
condition of the existence of a full-state observer is that observability matrix must
have full rank, that is
2
4
3
5
C
CA
CA
2
.
CA
N
1
rank
¼
N
(
5
:
85
)
In other words the system must be full-state observable.
x
(
k
+1)
y
(
k
)
x
(
k
)
Unit
delay
u
(
k
)
C
B
+
+
A
ˆ
x
(
k
)
ˆ
y
(
k
)
+
+
Unit
delay
-
+
C
+
ˆ
x
(
k
)
A
K
FIGURE 5.6
Block diagram of full-state observer.
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