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i
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s
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lt d
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C
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:
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Hig
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UCT
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Ov
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f
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m
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ce
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teg
r
ate
f
au
lt
d
etec
ti
o
n
an
d
d
iag
n
o
s
is
(
FDD)
to
o
ls
[1
]
,
[
2
]
to
m
ain
tain
,
f
o
r
a
lo
n
g
tim
e,
th
e
d
esire
d
p
er
f
o
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m
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ce
o
f
t
h
e
wh
o
le
s
y
s
tem
in
v
a
r
io
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s
s
ec
to
r
s
.
I
n
p
ar
ticu
lar
,
FDD
h
as
a
v
er
y
im
p
o
r
ta
n
t
r
o
le
in
m
o
n
ito
r
in
g
th
e
b
eh
a
v
io
r
o
f
s
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s
tem
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ar
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les
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d
r
ev
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f
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lts
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it
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o
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m
ed
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ased
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th
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r
elativ
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in
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o
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m
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to
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tem
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d
its
eq
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en
t.
T
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ca
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b
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ir
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ea
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tates
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s
er
v
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esti
m
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te
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m
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s
tates
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eq
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ir
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if
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to
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tate
m
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d
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ten
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b
ased
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its
s
t
ate
v
ar
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lin
k
ed
to
g
eth
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b
y
m
ath
em
atica
l
eq
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s
.
I
f
th
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p
r
o
ce
s
s
es
h
av
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co
n
s
tr
ain
ts
,
th
en
it
is
n
e
ce
s
s
ar
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to
u
s
e
s
tatic
eq
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atio
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s
to
s
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f
f
icien
tly
ch
ar
ac
ter
ize
th
e
s
tu
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ied
p
r
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ce
s
s
.
Su
ch
s
y
s
tem
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co
m
p
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s
ed
o
f
s
tatic
an
d
d
y
n
am
ic
eq
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n
s
a
r
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ca
lled
s
in
g
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lar
,
o
r
d
escr
ip
to
r
o
r
im
p
licit
s
y
s
te
m
s
[
3
]
.
R
ec
en
tly
,
th
e
FDD
p
r
o
b
lem
f
o
r
s
in
g
u
lar
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
S
ta
te
a
n
d
fa
u
lt e
s
tima
tio
n
b
a
s
ed
o
n
f
u
z
z
y
o
b
s
erver fo
r
a
cla
s
s
o
f Ta
ka
g
i
-
S
u
g
en
o
s
in
g
u
la
r
…
(
K
a
o
u
ta
r
Ou
a
r
id
)
173
s
y
s
tem
s
h
as
a
ttra
cted
m
u
ch
atten
tio
n
in
v
ar
io
u
s
f
ield
s
s
u
ch
as
m
ec
h
an
ical
en
g
in
ee
r
in
g
,
co
m
p
u
ter
s
cien
ce
,
civ
il e
n
g
i
n
ee
r
in
g
,
elec
tr
ical
en
g
in
ee
r
in
g
a
n
d
a
u
to
m
atio
n
.
Var
io
u
s
tech
n
iq
u
es
f
o
r
d
etec
t
in
g
an
d
esti
m
atin
g
f
au
lts
h
av
e
b
ee
n
p
r
o
p
o
s
ed
f
o
r
th
e
class
o
f
lin
ea
r
s
y
s
tem
s
[
4
]
,
[
5
]
,
an
d
f
o
r
th
e
c
lass
o
f
n
o
n
lin
ea
r
s
y
s
tem
s
[
6
]
-
[
8
]
allo
win
g
to
p
r
o
v
id
e
a
cl
o
s
er
r
ep
r
esen
tatio
n
to
th
e
r
ea
l
s
y
s
tem
,
b
u
t
wh
ich
ar
e
d
if
f
icu
lt
to
ex
p
lo
it.
Du
e
to
th
is
co
m
p
lex
ity
,
it
h
as
b
ec
o
m
e
ess
en
tial
to
wo
r
k
with
a
p
r
ec
is
e
class
o
f
n
o
n
lin
ea
r
s
y
s
tem
s
s
u
ch
as
L
ip
s
ch
itz
s
y
s
tem
s
,
u
n
ce
r
tain
s
y
s
tem
s
,
b
ilin
ea
r
s
y
s
tem
s
o
r
o
th
er
s
.
Fro
m
th
ese
class
es
o
f
n
o
n
lin
ea
r
s
y
s
tem
s
,
we
f
in
d
th
e
class
o
f
T
ak
a
g
i
-
Su
g
en
o
(
T
-
S)
[
9
]
n
o
n
lin
ea
r
s
y
s
tem
s
,
in
o
r
d
in
ar
y
o
r
s
in
g
u
l
ar
f
o
r
m
.
I
t
h
as
b
ee
n
in
tr
o
d
u
ce
d
to
co
m
p
r
o
m
is
e
b
etwe
en
th
e
g
o
o
d
p
r
ec
is
io
n
o
f
th
e
n
o
n
lin
ea
r
b
eh
a
v
io
r
o
f
th
e
s
tu
d
ied
s
y
s
tem
,
an
d
th
e
u
s
e
o
f
tech
n
iq
u
es
ad
a
p
ted
to
lin
ea
r
s
y
s
tem
s
d
u
e
to
th
e
co
n
v
ex
s
u
m
p
r
o
p
er
ty
o
f
its
ac
t
iv
atio
n
f
u
n
ctio
n
s
[
3
]
,
[
10
]
.
T
h
er
e
h
a
v
e
b
ee
n
m
a
n
y
m
eth
o
d
s
o
f
FDD
[
2
],
[
11
]
,
[
12
]
w
h
ich
ca
n
b
e
class
if
ied
in
to
s
ig
n
al
-
b
ased
ap
p
r
o
ac
h
es
[
13
]
,
k
n
o
wled
g
e
-
b
ased
ap
p
r
o
ac
h
es
[
12
]
,
[
1
4
]
,
an
d
p
r
o
ce
s
s
m
o
d
el
-
b
ased
ap
p
r
o
ac
h
es
[
12
]
,
[
13
]
wh
ich
co
n
tain
s
tate
o
b
s
er
v
er
-
b
ased
m
eth
o
d
r
e
p
r
esen
tin
g
an
an
aly
tical
m
eth
o
d
h
a
v
in
g
ac
h
i
ev
ed
s
ev
er
al
r
esu
lts
in
th
is
f
ield
,
an
d
wh
ich
d
ep
e
n
d
s
o
n
th
e
m
ath
em
atica
l
m
o
d
el
o
f
th
e
s
tu
d
ied
s
y
s
tem
wit
h
o
u
t
n
ee
d
i
n
g
o
th
er
co
m
p
o
n
en
ts
.
Ma
n
y
p
u
b
licatio
n
s
h
av
e
b
ee
n
in
ter
ested
in
th
e
d
esig
n
o
f
o
b
s
er
v
er
s
f
o
r
FDD
[
1
5
]
-
[
2
4
]
an
d
h
a
v
e
p
r
esen
ted
f
r
u
itfu
l
r
esu
lts
.
A
r
esid
u
al
g
en
er
ato
r
f
o
r
d
etec
tin
g
an
d
is
o
latin
g
ac
tu
ato
r
f
au
lts
f
o
r
a
class
o
f
T
-
S
f
u
zz
y
b
ilin
ea
r
s
y
s
tem
is
d
e
v
el
o
p
ed
i
n
[
18
]
.
Dev
elo
p
in
g
a
n
o
v
el
f
u
zz
y
FD
o
b
s
er
v
er
f
o
r
FD
o
f
s
en
s
o
r
s
f
a
u
lts
o
f
T
-
S
f
u
zz
y
s
y
s
tem
s
is
th
e
aim
o
f
th
e
wo
r
k
p
r
esen
ted
in
[
19
]
.
In
[
20
]
,
d
ep
icted
a
T
-
S
u
n
k
n
o
wn
in
p
u
t
o
b
s
er
v
er
to
s
im
u
ltan
eo
u
s
ly
esti
m
ate
th
e
in
ter
v
al
o
f
s
tates
an
d
ac
t
u
ato
r
f
a
u
lts
f
o
r
a
class
o
f
T
-
S
ex
p
licit
s
y
s
tem
s
.
An
o
th
er
tech
n
iq
u
e
b
ased
o
n
a
r
o
b
u
s
t
f
au
lt
esti
m
atio
n
o
b
s
er
v
er
h
as
b
ee
n
in
tr
o
d
u
ce
d
f
o
r
esti
m
atin
g
ac
tu
ato
r
f
au
l
ts
f
o
r
a
class
o
f
d
is
cr
ete
-
ti
m
e
s
in
g
u
lar
s
y
s
tem
s
[
21
]
.
I
n
[
22
]
,
a
d
esig
n
o
f
a
n
a
d
ap
tiv
e
o
b
s
er
v
er
is
p
r
o
p
o
s
ed
f
o
r
d
etec
tin
g
s
en
s
o
r
f
au
lts
o
f
an
in
d
u
s
tr
ial
s
er
v
o
s
y
s
tem
.
Fo
r
th
e
f
au
lt
d
iag
n
o
s
is
an
d
r
ec
o
n
s
tr
u
ctio
n
o
f
th
e
f
au
lts
af
f
ec
tin
g
th
e
s
tates
o
f
t
h
e
s
y
s
tem
,
in
[
23
]
s
u
g
g
ested
a
n
ew
au
g
m
en
ted
lin
ea
r
p
a
r
a
m
eter
-
v
ar
y
i
n
g
(
L
PV
)
o
b
s
er
v
er
f
o
r
a
class
o
f
L
PV
m
o
d
els.
T
h
e
d
e
s
i
g
n
o
f
a
c
o
m
b
i
n
a
t
i
o
n
o
f
r
e
d
u
c
e
d
-
o
r
d
e
r
L
P
V
a
n
d
f
u
l
l
-
o
r
d
e
r
L
P
V
u
n
k
n
o
w
n
i
n
p
u
t
o
b
s
e
r
v
e
r
s
,
r
e
s
p
e
c
t
i
v
el
y
,
f
o
r
F
D
D
o
f
a
c
t
u
at
o
r
a
n
d
s
e
n
s
o
r
f
a
u
l
t
s
o
f
i
n
d
u
s
t
r
i
a
l
p
r
o
c
es
s
es
is
p
r
e
s
e
n
t
e
d
i
n
[
24
]
.
Mo
s
t o
f
th
ese
o
b
s
er
v
er
s
ar
e
s
y
n
th
esized
to
esti
m
ate
o
n
ly
ac
t
u
ato
r
o
r
s
en
s
o
r
f
au
lts
wh
ile
g
u
ar
an
teein
g
asy
m
p
to
tic
co
n
v
e
r
g
en
ce
f
o
r
v
ar
io
u
s
class
o
f
n
o
n
lin
ea
r
s
y
s
tem
in
co
n
tin
u
o
u
s
o
r
d
is
cr
ete
-
ti
m
e.
T
h
e
g
o
al
o
f
o
u
r
wo
r
k
is
n
o
t
to
co
m
p
a
r
e
o
u
r
ap
p
r
o
ac
h
with
t
h
o
s
e
alr
ea
d
y
ca
r
r
ied
o
u
t,
b
u
t
r
ath
e
r
to
e
x
ten
d
o
u
r
r
esu
lts
f
r
o
m
th
e
ca
s
e
o
f
s
in
g
u
lar
lin
ea
r
m
o
d
el
s
[
25
]
a
n
d
T
-
S
s
in
g
u
lar
m
o
d
e
ls
with
m
ea
s
u
r
ab
le
p
r
em
is
e
v
ar
iab
les
[
26
]
to
th
e
ca
s
e
o
f
T
-
S
s
in
g
u
lar
m
o
d
els
with
u
n
m
ea
s
u
r
ab
l
e
p
r
em
is
e
v
ar
iab
les
wh
ile
en
s
u
r
i
n
g
an
ex
p
o
n
en
tial
co
n
v
er
g
en
ce
,
an
d
s
im
u
ltan
eo
u
s
ly
esti
m
atin
g
th
e
u
n
m
ea
s
u
r
ab
le
s
tates
an
d
th
e
f
au
lts
at
t
h
e
lev
el
o
f
ac
tu
ato
r
s
an
d
s
en
s
o
r
s
.
I
n
th
is
wo
r
k
,
f
o
r
s
im
u
ltan
eo
u
s
esti
m
atio
n
o
f
s
tates
an
d
f
au
lts
,
th
e
n
o
v
el
s
u
g
g
ested
t
ec
h
n
iq
u
e
co
n
s
is
ts
to
as
s
o
ciate
f
o
r
ea
ch
lo
ca
l
m
o
d
el
a
lo
ca
l
o
b
s
er
v
er
.
T
h
en
,
th
e
p
r
o
p
o
s
ed
f
u
zz
y
o
b
s
er
v
er
is
o
b
tain
ed
b
y
an
ag
g
r
e
g
atio
n
o
f
th
e
l
o
ca
l
o
b
s
er
v
er
s
.
Ou
r
co
n
tr
ib
u
tio
n
is
b
ased
o
n
th
e
s
ep
a
r
atio
n
o
f
th
e
d
y
n
am
ic
e
q
u
atio
n
s
f
r
o
m
th
e
s
tatic
eq
u
atio
n
s
wh
i
ch
m
ak
es
it
p
o
s
s
ib
le
to
f
ac
il
itat
e
an
d
m
in
im
ize
th
e
co
m
p
u
tati
o
n
b
y
o
b
tain
i
n
g
th
e
s
tatic
s
tate
s
ju
s
t
f
r
o
m
th
e
d
y
n
am
ic
s
tates
alr
ea
d
y
f
o
u
n
d
.
T
h
e
d
esig
n
c
o
n
d
itio
n
s
ar
e
ex
p
r
ess
ed
in
ter
m
s
o
f
L
MI
s
.
T
h
is
o
b
s
er
v
er
is
ap
p
lie
d
f
o
r
b
o
t
h
ac
tu
ato
r
s
a
n
d
s
en
s
o
r
s
f
au
lts
f
o
r
a
class
o
f
T
-
S
s
in
g
u
lar
m
o
d
el
in
t
h
e
ca
s
e
o
f
u
n
m
ea
s
u
r
ab
le
p
r
em
is
e
v
ar
iab
les.
T
h
e
p
ap
e
r
is
co
m
p
o
s
ed
o
f
f
iv
e
p
ar
ts
th
at
ar
e
p
r
e
s
en
ted
as
f
o
llo
ws:
Sectio
n
2
ex
p
o
s
es
th
e
class
o
f
th
e
s
tu
d
ied
s
y
s
tem
.
Sectio
n
3
p
r
o
v
id
es
th
e
s
y
n
th
esis
o
f
th
e
p
r
o
p
o
s
ed
o
b
s
er
v
er
an
d
th
e
s
tab
ilit
y
co
n
d
itio
n
s
.
T
h
e
n
u
m
er
ical
r
esu
lts
o
f
th
e
a
p
p
licatio
n
ex
am
p
le
ar
e
g
iv
en
in
s
ec
tio
n
4
.
Sectio
n
5
is
d
ev
o
ted
to
a
b
r
ief
c
o
n
clu
s
io
n
.
2.
M
AT
H
E
M
AT
I
CA
L
F
O
RM
UL
A
T
I
O
N
O
F
T
H
E
CO
N
SI
DE
R
E
D
M
O
D
E
L
I
n
th
is
p
a
p
er
,
t
h
e
f
o
llo
win
g
class
o
f
c
o
n
ti
n
u
o
u
s
-
t
ime
Tak
a
g
i
-
S
u
g
e
n
o
sin
g
u
lar
m
o
d
e
l
(
C
T
SS
M
)
with
u
n
m
ea
s
u
r
ab
le
p
r
em
is
e
v
ar
iab
l
es in
p
r
esen
ce
o
f
ac
tu
ato
r
a
n
d
s
en
s
o
r
f
au
lt is
co
n
s
id
er
ed
(
1
)
,
{
̇
=
∑
(
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=
1
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+
+
)
=
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(
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1
(
+
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)
(
1
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w
h
er
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=
[
1
2
]
∈
ℝ
is
th
e
s
tate
v
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to
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with
1
∈
ℝ
is
th
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v
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v
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2
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with
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12
21
22
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(
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3
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,
…
,
(
4
)
t
h
e
m
atr
ix
wh
o
s
e
(
)
=
<
is
ass
u
m
ed
to
h
av
e
th
e
f
o
l
lo
win
g
f
o
r
m
,
=
(
0
0
0
)
(
5
)
Ass
u
m
p
tio
n
1
:
Ass
u
m
e
th
at
[
3
]
:
−
(
,
)
ar
e
r
eg
u
lar
,
i.e
.
d
et
(
−
)
≠
0
∀
ℂ
−
T
h
e
s
u
b
-
m
o
d
els (
3
)
a
r
e
im
p
u
ls
e
o
b
s
er
v
ab
le
a
n
d
d
etec
tab
le
T
h
e
s
ep
ar
atio
n
o
f
th
e
d
y
n
am
ic
eq
u
atio
n
s
f
r
o
m
th
e
s
tatic
eq
u
atio
n
in
ea
c
h
s
u
b
-
m
o
d
el
(
3
)
is
th
e
aim
o
f
o
u
r
ap
p
r
o
ac
h
,
an
d
th
e
n
th
e
ag
g
r
eg
atio
n
o
f
th
e
r
esu
ltin
g
s
u
b
-
m
o
d
els
allo
ws
o
b
tain
in
g
th
e
g
lo
b
al
f
u
zz
y
m
o
d
el.
So
,
u
s
in
g
th
e
ex
p
r
ess
io
n
o
f
th
e
m
atr
ices
(
2
)
an
d
(
5
)
,
th
e
s
u
b
-
m
o
d
el
(
3
)
ca
n
b
e
wr
itten
in
th
e
f
o
llo
win
g
s
ec
o
n
d
eq
u
iv
alen
t f
o
r
m
[
3
]
,
{
̇
1
=
11
1
+
12
2
+
1
+
1
0
=
21
1
+
22
2
+
2
+
2
=
1
1
+
2
2
+
+
+
(
6
)
b
y
f
in
d
in
g
th
e
ex
p
r
ess
io
n
o
f
th
e
s
tatic
v
ar
iab
le
Z
2
,
an
d
r
ep
lacin
g
it in
(
6
)
,
we
o
b
tain
,
{
̇
1
=
1
+
+
2
=
1
+
+
=
1
+
+
+
(
7
)
w
h
er
e
,
{
=
11
+
12
=
1
+
12
=
1
+
12
=
−
22
−
1
21
=
−
22
−
1
2
=
−
22
−
1
2
=
1
+
2
=
+
2
=
+
2
(
8
)
l
et
d
ef
in
e
,
=
(
)
(
9
)
w
h
ich
is
eq
u
iv
alen
t to
t
h
e
f
o
ll
o
win
g
s
tate
r
ep
r
esen
tatio
n
,
{
̇
1
=
1
+
+
2
=
1
+
+
=
1
+
+
(
1
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
S
ta
te
a
n
d
fa
u
lt e
s
tima
tio
n
b
a
s
ed
o
n
f
u
z
z
y
o
b
s
erver fo
r
a
cla
s
s
o
f Ta
ka
g
i
-
S
u
g
en
o
s
in
g
u
la
r
…
(
K
a
o
u
ta
r
Ou
a
r
id
)
175
wh
er
e
,
{
=
(
0
)
=
(
0
)
=
(
)
(
1
1
)
t
h
en
,
f
r
o
m
(
1
0
)
ρ
i
(
β
)
ca
n
b
e
r
ewr
itten
as
,
(
)
=
(
1
,
2
=
1
+
+
)
=
(
1
,
,
)
=
(
⍵
)
(
1
2
)
w
ith
⍵
=
[
1
]
.
So
,
th
e
s
y
s
tem
(
1
)
ca
n
b
e
r
ewr
itten
u
n
d
e
r
th
e
f
o
llo
win
g
eq
u
iv
ale
n
t f
o
r
m
,
{
̇
1
=
∑
(
⍵
)
=
1
(
1
+
+
)
2
=
∑
(
⍵
)
=
1
(
1
+
+
)
=
∑
(
⍵
)
=
1
(
1
+
+
)
(
1
3
)
Ass
u
m
p
tio
n
2
:
Ass
u
m
e
th
at
is
c
o
n
s
id
er
ed
i
n
th
e
f
o
llo
win
g
f
o
r
m
,
=
0
+
1
+
2
2
+
⋯
+
(
1
4
)
w
h
er
e
;
=
0
,
1
,
…
,
ar
e
r
ea
l
u
n
k
n
o
wn
c
o
n
s
tan
t
p
ar
am
eter
s
an
d
th
e
(
+
1
)
ℎ
tim
e
d
er
iv
ativ
e
o
f
t
h
e
f
au
lt is
n
u
ll.
L
et
,
=
−
1
with
=
1
,
…
,
+
1
(
1
5
)
t
h
en
,
{
̇
=
+
1
̇
+
1
=
0
with
=
1
,
…
,
(
1
6
)
t
h
u
s
,
we
r
ewr
ite
th
e
s
y
s
tem
(
1
3
)
u
n
d
er
th
e
eq
u
iv
ale
n
t
au
g
m
e
n
ted
s
tate
f
o
r
m
as f
o
llo
ws,
{
̇
1
=
∑
(
)
=
1
(
̃
1
+
̃
)
2
=
∑
(
)
=
1
(
̃
1
+
)
=
∑
(
)
=
1
(
̃
1
+
)
(
1
7
)
w
h
er
e
,
{
1
=
(
1
1
⋯
)
2
=
2
=
(
1
)
̃
=
(
0
⋯
0
0
0
⋯
0
⋮
⋱
⋱
⋱
⋮
0
0
0
⋯
0
0
⋯
0
0
)
̃
=
(
0
0
⋯
0
)
̃
=
(
0
⋯
0
)
̃
=
(
0
⋯
0
)
(
1
8
)
3.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
e
f
o
llo
win
g
s
ec
tio
n
s
h
o
ws
th
e
d
esig
n
o
f
n
ew
s
tr
u
ctu
r
e
o
f
f
u
zz
y
o
b
s
er
v
er
allo
win
g
th
e
s
im
u
ltan
eo
u
s
esti
m
atio
n
o
f
th
e
u
n
m
ea
s
u
r
ab
le
s
tates
an
d
u
n
k
n
o
wn
f
a
u
lts
o
f
th
e
eq
u
i
v
alen
t
s
t
r
u
ctu
r
e
(
1
7
)
o
f
th
e
C
T
SS
M
(
1
)
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
25
,
No
.
1
,
J
an
u
ar
y
20
22
:
1
72
-
1
82
176
{
̂
1
̇
=
∑
(
̂
)
=
1
(
̃
̂
1
+
̃
−
(
̂
−
)
)
̂
2
=
∑
(
̂
)
=
1
(
̃
̂
1
+
)
̂
=
∑
(
̂
)
=
1
(
̃
̂
1
+
)
(
1
9
)
s
u
ch
th
at
th
e
esti
m
ated
v
ec
to
r
s
o
f
(
1
,
2
)
an
d
y
ar
e
d
en
o
ted
b
y
(
̂
1
,
̂
2
)
an
d
y
̂
,
r
esp
ec
tiv
ely
.
Fo
r
=
1
,
⋯
,
th
e
ter
m
ex
p
r
ess
es
th
e
o
b
s
er
v
er
g
ain
f
o
r
th
e
ℎ
s
u
b
m
o
d
e
l
s
u
ch
as
th
e
esti
m
ated
o
f
th
e
au
g
m
en
ted
v
ec
to
r
o
f
th
e
s
tates a
n
d
f
au
lts
ten
d
s
asy
m
p
t
o
tically
to
war
d
s
th
e
r
ea
l v
ec
to
r
.
Def
in
in
g
,
=
(
1
2
)
=
(
̂
1
−
1
̂
2
−
2
)
(
2
0
)
s
u
b
s
titu
tin
g
(
1
7
)
a
n
d
(
1
9
)
in
t
o
(
2
0
)
g
iv
es
th
e
f
o
llo
win
g
s
tatic
an
d
d
y
n
am
ic
eq
u
atio
n
s
o
f
th
e
s
tate
esti
m
atio
n
er
r
o
r
,
{
̇
1
=
∑
(
̂
)
=
1
(
̃
̂
1
+
̃
−
(
̂
−
)
)
−
∑
(
)
=
1
(
̃
1
+
̃
)
2
=
∑
(
̂
)
=
1
(
̃
̂
1
+
)
−
∑
(
)
=
1
(
̃
1
+
)
(
2
1
)
e
q
u
iv
alen
t
to
,
{
̇
1
=
∑
(
̂
)
=
1
(
̃
1
−
(
̂
−
)
)
−
∑
(
(
)
−
(
̂
)
)
=
1
(
̃
1
+
̃
)
2
=
∑
(
̂
)
=
1
̃
1
−
∑
(
(
)
−
(
̂
)
)
=
1
(
̃
1
+
)
(
2
2
)
l
et
co
n
s
id
er
ℱ
=
̃
,
̃
,
̃
,
an
d
,
∑
(
(
)
−
(
̂
)
)
ℱ
=
=
1
∑
(
)
(
̂
)
,
=
1
∆
ℱ
(
23)
w
ith
∆
ℱ
=
ℱ
−
ℱ
.
T
h
en
,
b
y
u
s
in
g
t
h
e
ex
p
r
ess
io
n
(
2
3
)
th
e
s
y
s
tem
(
2
2
)
b
ec
o
m
es
,
{
̇
1
=
∑
(
̂
)
=
1
(
̃
1
−
(
̂
−
)
)
−
∑
(
)
(
̂
)
,
=
1
(
∆
̃
1
+
∆
̃
)
2
=
∑
(
̂
)
=
1
̃
1
−
∑
(
)
(
̂
)
,
=
1
(
∆
̃
1
+
∆
)
(
2
4
)
a
s
∑
(
)
=
1
=
1
,
we
o
b
tain
,
{
̇
1
=
∑
(
)
(
̂
)
,
=
1
(
̃
1
−
(
̂
−
)
)
−
∑
(
)
(
̂
)
,
=
1
(
∆
̃
1
+
∆
̃
)
2
=
∑
(
)
(
̂
)
,
=
1
(
̃
1
−
∆
̃
1
−
∆
)
(
2
5
)
i
n
th
e
s
am
e
way
,
we
ca
n
g
et
an
d
̂
as
f
o
llo
ws,
{
=
∑
(
)
ℎ
(
̂
)
,
ℎ
=
1
(
(
̃
ℎ
+
∆
̃
ℎ
)
1
+
(
ℎ
+
∆
ℎ
)
)
̂
=
∑
(
)
ℎ
(
̂
)
,
ℎ
=
1
(
̃
ℎ
̂
1
+
ℎ
)
(
2
6
)
w
ith
∆
̃
ℎ
=
̃
−
̃
ℎ
an
d
∆
ℎ
=
−
ℎ
.
B
y
th
e
s
u
b
s
titu
tio
n
o
f
(
2
6
)
in
(
2
5
)
,
we
g
et
,
{
̇
1
=
∑
(
)
(
̂
)
ℎ
(
̂
)
,
,
ℎ
=
1
(
ℎ
1
+
ℎ
1
+
ℎ
)
2
=
∑
(
)
(
̂
)
,
=
1
(
̃
1
−
∆
̃
1
−
∆
)
(
2
7
)
w
ith
,
{
ℎ
=
̃
−
̃
ℎ
ℎ
=
∆
̃
ℎ
−
∆
̃
ℎ
=
∆
ℎ
−
∆
̃
,
,
ℎ
(
1
,
⋯
,
)
(
2
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
S
ta
te
a
n
d
fa
u
lt e
s
tima
tio
n
b
a
s
ed
o
n
f
u
z
z
y
o
b
s
erver fo
r
a
cla
s
s
o
f Ta
ka
g
i
-
S
u
g
en
o
s
in
g
u
la
r
…
(
K
a
o
u
ta
r
Ou
a
r
id
)
177
t
h
er
ef
o
r
e
,
to
d
em
o
n
s
tr
ate
th
e
co
n
v
er
g
en
ce
o
f
to
war
d
s
ze
r
o
,
it
s
u
f
f
ices
to
d
em
o
n
s
tr
ate
th
at
1
co
n
v
er
g
es
to
ze
r
o
.
C
o
n
s
id
er
in
g
̃
1
=
(
1
1
)
,
we
g
et
,
{
̃
1
̇
=
∑
(
)
(
̂
)
ℎ
(
̂
)
,
,
ℎ
=
1
(
ℎ
̃
1
+
ℎ
)
1
=
̃
1
(
2
9
)
w
ith
,
{
ℎ
=
(
ℎ
ℎ
0
̃
)
ℎ
=
(
ℎ
̃
)
=
(
0
)
(
3
0
)
g
u
ar
an
teein
g
th
e
s
tab
ilit
y
o
f
(
2
9
)
wh
ile
atten
u
atio
n
g
t
h
e
ef
f
ec
t
o
f
on
1
is
lin
k
ed
to
th
e
d
et
er
m
in
atio
n
o
f
th
e
o
b
s
er
v
er
g
ain
s
f
o
r
=
1
,
⋯
,
.
T
h
eo
r
em
:
Un
d
er
ass
u
m
p
tio
n
s
1
an
d
2
,
if
f
o
r
th
e
C
T
SS
M
(
1
)
th
e
r
e
ar
e
m
at
r
ices
1
,
2
,
f
o
r
=
1
,
⋯
,
,
an
d
a
p
o
s
itiv
e
s
ca
lar
ξ
f
o
r
a
g
iv
en
>
0
wh
ich
s
atis
f
y
th
e
L
MI
s
(
3
1
)
,
th
e
n
it
will
b
e
p
o
s
s
ib
le
t
o
d
eter
m
in
e
th
e
o
b
s
er
v
er
g
ain
s
,
th
at
en
s
u
r
e
th
e
e
x
p
o
n
en
tial c
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ce
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r
o
o
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th
e
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m
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r
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o
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et
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llo
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ilit
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d
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n
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id
er
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I
SS
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:
2
5
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2
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4
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2
I
n
d
o
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esian
J
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lec
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n
g
&
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o
m
p
Sci
,
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l.
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1
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an
u
ar
y
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22
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72
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o
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ak
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u
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t (
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8
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6
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d
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llo
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4
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e
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ed
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ce
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e
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1
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p
r
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e
T
h
eo
r
em
th
at
co
m
p
lete
th
e
p
r
o
o
f
.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
o
d
is
p
lay
th
e
b
e
n
ef
its
o
f
th
e
s
u
g
g
ested
o
b
s
er
v
er
,
we
co
n
s
id
er
th
e
f
o
llo
win
g
C
T
SS
M
wh
ich
is
af
f
ec
ted
b
y
f
au
lts
,
at
th
e
lev
el
o
f
ac
tu
ato
r
an
d
s
en
s
o
r
,
an
d
s
u
b
jec
ted
t
o
u
n
m
ea
s
u
r
ab
le
p
r
em
is
e
v
ar
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le,
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)
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5
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w
h
er
e
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ℝ
4
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d
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ℝ
ar
e
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e
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o
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tates,
in
p
u
t,
o
u
tp
u
t,
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tu
at
o
r
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lt
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u
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;
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ep
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t
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weig
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g
f
u
n
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n
s
,
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1
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h
er
e
th
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p
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n
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h
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r
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v
ar
iab
le
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=
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5
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5
1
2
2
∈
[
,
]
(
4
9
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i
n
o
r
d
er
to
ap
p
ly
th
e
s
u
g
g
ested
f
u
zz
y
o
b
s
er
v
e
r
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1
9
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n
o
u
r
ap
p
licatio
n
ex
am
p
le
(
4
5
)
,
it
s
u
f
f
ices
to
r
ep
r
esen
t
it
in
its
eq
u
iv
alen
t
f
o
r
m
(
1
7
)
.
T
h
u
s
,
b
y
u
s
in
g
th
e
T
h
eo
r
e
m
with
=
0
.
1
,
we
o
b
tain
th
e
f
o
llo
win
g
o
b
s
er
v
er
g
ai
n
s
1
an
d
2
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
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SS
N:
2502
-
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5
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t
h
e
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im
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latio
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iv
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n
in
F
ig
u
r
es 1
t
o
4
wh
e
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e
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e
i
n
p
u
t sig
n
al
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e
n
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y
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(
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=
{
−
2
ℎ
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2
0
(
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1
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Un
d
er
Ass
u
m
p
tio
n
2
,
th
e
t
r
a
jecto
r
ies
o
f
ac
tu
ato
r
an
d
s
en
s
o
r
f
au
lt
s
ig
n
als,
wh
ic
h
ar
e
a
p
p
lied
r
esp
ec
tiv
ely
d
u
r
in
g
th
e
in
ter
v
als
[
4
0
,
1
6
0
s
]
an
d
[
2
0
0
,
3
2
0
s
]
,
th
eir
f
i
r
s
t
o
r
d
er
d
er
i
v
ativ
es,
an
d
t
h
eir
esti
m
ates
ar
e
s
h
o
wn
in
Fi
g
u
r
es 3
an
d
4
.
T
h
ese
r
esu
lts
d
em
o
n
s
tr
ate
th
at
th
e
s
u
g
g
ested
f
u
zz
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b
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er
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e
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g
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o
d
p
e
r
f
o
r
m
an
ce
s
in
esti
m
atin
g
u
n
m
ea
s
u
r
ab
le
s
tates
an
d
u
n
k
n
o
wn
f
au
lts
wh
ile
ca
tch
i
n
g
u
p
with
u
n
wan
ted
v
ar
iatio
n
s
.
T
h
i
s
ap
p
r
o
ac
h
h
as
th
e
b
en
ef
it
o
f
b
ei
n
g
ap
p
lied
at
th
e
lev
el
o
f
a
lar
g
e
class
o
f
n
o
n
li
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s
y
s
tem
s
.
T
h
is
is
d
u
e
to
t
h
e
f
ac
t
th
at
it
is
n
o
t
r
eq
u
ir
ed
to
k
n
o
w
th
e
v
al
u
e
o
f
th
e
L
ip
s
ch
itz
co
n
s
tan
t
th
at
ca
n
in
f
lu
en
ce
th
e
r
eso
lu
tio
n
o
f
L
MI
s
[
2
7
]
,
as
well
as
with
o
u
t b
ein
g
lim
ited
b
y
t
h
e
c
o
n
d
itio
n
o
f
th
e
r
an
k
b
etwe
en
t
h
e
m
atr
ices su
ch
as in
[
2
8
]
.
Fig
u
r
e
1
.
z
1
an
d
z
2
with
th
eir
esti
m
ates
Fig
u
r
e
2
.
z
3
an
d
z
4
with
th
eir
esti
m
ates
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
25
,
No
.
1
,
J
an
u
ar
y
20
22
:
1
72
-
1
82
180
Fig
u
r
e
3
.
an
d
̇
with
th
eir
esti
m
ates
Fig
u
r
e
4
.
an
d
̇
with
th
eir
esti
m
ates
5.
CO
NCLU
SI
O
N
T
h
is
wo
r
k
is
a
d
d
r
ess
ed
to
th
e
d
esig
n
o
f
f
u
zz
y
o
b
s
er
v
er
f
o
r
s
im
u
ltan
eo
u
s
esti
m
atio
n
o
f
u
n
m
ea
s
u
r
ab
le
s
tates
an
d
u
n
k
n
o
w
n
f
a
u
lts
,
f
o
r
T
a
k
ag
i
-
Su
g
e
n
o
s
in
g
u
lar
m
o
d
els
in
co
n
tin
u
o
u
s
tim
e.
T
h
e
m
ain
id
ea
o
f
th
is
p
ap
er
is
to
e
x
ten
d
t
h
e
r
esu
l
ts
d
ev
elo
p
ed
i
n
th
e
ca
s
e
o
f
m
ea
s
u
r
ab
le
p
r
em
is
e
v
ar
iab
l
es.
T
h
e
d
iag
n
o
s
tic
p
r
o
ce
d
u
r
e
is
b
ased
o
n
th
e
s
ep
ar
atio
n
o
f
s
tatic
eq
u
atio
n
s
f
r
o
m
d
y
n
am
ic
o
n
es.
Usi
n
g
th
is
,
t
h
e
d
eter
m
i
n
atio
n
o
f
th
e
s
tatic
v
ar
iab
les
will
b
e
d
e
d
u
ce
d
f
r
o
m
th
e
c
o
m
p
u
tatio
n
o
f
th
e
d
y
n
a
m
ic
v
ar
ia
b
les.
At
la
s
t,
an
ex
am
p
le
o
f
ap
p
licatio
n
is
p
r
esen
ted
in
o
r
d
er
to
h
ig
h
lig
h
t
a
n
d
c
o
n
f
ir
m
t
h
e
ef
f
ec
tiv
e
n
ess
o
f
t
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
in
th
e
esti
m
atio
n
o
f
th
e
s
tates,
an
d
th
e
f
au
lts
o
f
ac
tu
ato
r
s
an
d
s
en
s
o
r
s
.
RE
F
E
R
E
NC
E
S
[1
]
Y.
-
J.
P
a
r
k
,
S
.
-
K
S
.
F
a
n
,
a
n
d
C
.
-
Y
.
H
su
,
"
A
R
e
v
i
e
w
o
n
F
a
u
l
t
D
e
t
e
c
t
i
o
n
a
n
d
P
r
o
c
e
ss
D
i
a
g
n
o
s
t
i
c
s
i
n
I
n
d
u
st
r
i
a
l
P
r
o
c
e
ss
e
s,"
Pro
c
e
sses
,
v
o
l
.
8
,
n
o
.
9
,
p
p
.
1
-
2
6
,
2
0
2
0
,
d
o
i
:
1
0
.
3
3
9
0
/
p
r
8
0
9
1
1
2
3
.
[2
]
R
.
A
r
u
n
t
h
a
v
a
n
a
t
h
a
n
n
,
F
.
K
h
a
n
,
S
.
A
h
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