Image Processing Reference
In-Depth Information
The observability matrix P is
2
4
3
5 ¼
2
4
3
5
C
CA
CA 2
1
0
2
P ¼
3
:
53
1
:
6
1
:
95 0
:
35
1
:
72
Since det (P)
¼
3
:
53
0, P is full rank and the system is completely state
observable.
Example 4.19
Consider the MIMO system
2
4
3
5
2
4
3
5
100
010
001
10
01
"
#
u 1 (k)
u 2 (k)
x(k þ
1)
¼
x(k)
þ
12
"
# x(k)
101
110
y(k)
¼
The observability matrix P is
2
4
3
5
101
110
2
4
3
5 ¼
C
CA
CA 2
101
110
P ¼
101
110
Since rank(P)
¼
2, P
is not
full rank and the system is not completely state
observable.
Example 4.20
Consider the MIMO system
2
4
3
5 x(k)
2
4
3
5
1
10
00
10
u 1 (k)
u 2 (k)
x(k þ
1)
¼
:
51
þ
31
100
:
6
10
x(k)
111
110
y(k)
¼
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