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figures consider the fuzzy bilinear models and the nonlinear system. They
illustrate the superposition of the nonlinear states with those coming from the T-S
bilinear models representation. We can see that the fuzzy bilinear models well
approximate the nonlinear dynamic behavior.
These
5.2 State Estimation Design
The observer gains are obtained by solving the LMIs ( 38 ) under constraints ( 39 ),
( 40 ) and ( 41 ). By choosing the scalar
c ¼
0
:
895, their obtained observer gains are:
1
:
160
0
:
474
0
:
013
H 1 ¼
;
L 1 ¼
;
0
:
264
0
:
311
0
:
005
;
0
0
0
:
177
J 1 ¼
M 1 ¼
0
:
071
31
:
057
75
:
54
0
:
072
;
;
H 2 ¼
L 2 ¼
12
:
223
29
:
716
0
:
029
;
0
0
0
:
177
J 2 ¼
M 2 ¼
0
:
071
3
:
033
3
:
083
0
:
342
H 3 ¼
; L 3 ¼
;
1
:
013
0
:
733
0
:
137
;
0
0
0
:
177
J 3 ¼
M 3 ¼
0
:
071
1
:
315
0
:
890
0
:
287
H 4 ¼
;
L 4 ¼
;
:
:
:
0
326
0
856
0
115
;
:
0
0
0
177
J 4 ¼
M 4 ¼
;
0
:
071
428
0 : 829
0
:
E
¼
;
Then, Figs. 9 and 10 show respectively the evolution of the actual system states
and their corresponding observer ones for initial conditions given by x 0 ¼½
T
0
:
51
and x 0 ¼
0.
It can be deduced from these Figs. 9 and 10 that the proposed observer succeeds
to track the system trajectories in spite of the presence of the unknown input and
with unmeasurable decision variables.
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