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functions depend on the
first component of the estimated state vector
x 1 ð t Þ
. Then,
the weighting functions is described as follows:
Þ ¼ l i ^
ð
x 1 ð
t
Þ
Þ
h i x 1 ð
ð
Þ
t
P j¼1 l j ^
ð
x 1 t
ðÞ
Þ
where
l i ^
ð
x 1 ð
t
Þ
Þ
are de
ned by
ð ^
x 1 þ
5
2
l 1 ð^
x 1 ð
t
ÞÞ ¼
exp
ð
1
=
2
Þ
Þ
2
ð ^
x 1
5
2
l 2 ð x 1 ð t ÞÞ ¼
exp
ð
1
=
2
Þ
Þ
2
Thus, the resolution of the conditions of Theorem 2 leads to the following
matrix:
2
3
0
:
061
0
:
299
0
:
030
4
5
10 4
P
¼
0
:
299
1
:
495
0
:
006
0
:
030
0
:
006
1
:
554
Therefore, the observer gains are computed from ( 42 )to( 46 ) as follows:
2
3
1
:
337
3
:
566
4
5
E
¼
1
:
268
0
:
713
0
:
127
1
:
071
2
3
2
3
20
:
702
39
:
709
10
:
556
31
:
701
4
5 ;
4
5
L 1 ¼
4
:
140
7
:
942
L 2 ¼
2
:
111
6
:
340
0
:
414
0
:
794
0
:
211
0
:
634
2
3
2
3
1
:
268
2
:
806
4
5 ;
4
5
J 1 ¼
0
:
254
J 2 ¼
0
:
561
0
:
026
0
:
056
2
3
0
:
718
2
:
273
4
5
M 1 ¼
M 2 ¼
0
:
144
0
:
455
0
:
0143
0
:
046
2
3
2
3
14
:
445
5
:
607
9
:
443
10
:
546
4
:
309
7
:
513
4
5 ;
4
5
H 1 ¼
2
:
795
0
:
620
2
:
191
H 2 ¼
2
:
009
0
:
362
1
:
503
0
:
221
0
:
179
0
:
310
0
:
201
0
:
086
0
:
350
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