Image Processing Reference
In-Depth Information
Since the observability matrix is full rank, the system is completely state observ-
able. The observer gain vector K
e
is given by
2
4
3
5
2
4
3
5
1
C
CA
CA
2
.
CA
N1
0
0
.
0
1
1
C
CA
0
1
¼ A
2
K
e
¼ P(A)
0
:
2A þ
0
:
01I
10
01
¼
0
:
71
1
:
5
0
1
1
:
5
¼
1
:
08
1
:
84
1
:
84
The dynamics of the state feedback and observer are given by
x(k)
x(k)
x(k þ
1)
A
BK
f
¼
x(k þ
1)
K
e
CA
BK
f
K
e
C
or
2
4
3
5
¼
2
4
3
5
2
4
3
5
x
1
(k þ
1)
0
1
0
0
x
1
(k)
x
2
(k)
x
1
(k)
x
2
(k)
x
2
(k þ
1)
0
:
72 1
:
70
:
66
1
:
2
x
1
(k þ
1)
1
:
50
1
:
51
x
2
(k þ
1)
1
:
84
0
1
:
90
:
5
T
are shown in
The states of the system with initial conditions of x(0)
¼
½
12
Figures 5.8 and 5.9.
3
State
x
1
(
k
)
2.5
2
State
x
1
(
k
)
ˆ
1.5
1
0.5
0
0
2
4
6
8
10
12
14
k
FIGURE 5.8
Combined state estimator and state feedback (first state).
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