I
AE
S In
t
er
na
t
io
na
l J
o
urna
l o
f
Ro
bo
t
ics a
nd
Aut
o
m
a
t
io
n
(
I
J
RA)
Vo
l.
1
4
,
No
.
2
,
J
u
n
e
20
2
5
,
p
p
.
214
~
2
26
I
SS
N:
2722
-
2
5
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6
,
DOI
:
1
0
.
1
1
5
9
1
/i
jr
a
.
v
14
i
2
.
pp
2
1
4
-
2
26
214
J
o
ur
na
l ho
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ep
a
g
e
:
h
ttp
:
//ij
r
a
.
ia
esco
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co
m
Desig
n of
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∞
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sed fault
dete
ct
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n f
ilter
f
o
r l
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tain
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stems us
ing
line
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r ma
trix inequa
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ities
M
a
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a
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1,
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,
Ro
s
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iwa
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a
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R
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No
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2
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4
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r
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On
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t
c
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s
in
m
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-
b
a
se
d
fa
u
lt
d
e
tec
ti
o
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is
a
c
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g
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b
u
stn
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a
g
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in
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m
o
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u
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rtain
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e
s
wh
il
e
e
n
su
rin
g
se
n
siti
v
it
y
to
fa
u
l
ts.
Th
is
st
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d
y
p
ro
p
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s
a
n
o
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ti
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ize
d
a
p
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r
d
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n
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u
lt
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e
tec
ti
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ters
f
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d
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re
te
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ti
m
e
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n
e
a
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sy
ste
m
s
with
n
o
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b
o
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n
d
e
d
m
o
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e
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n
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rtain
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e
s.
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h
e
d
e
sig
n
lev
e
ra
g
e
s
th
e
H
-
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o
p
ti
m
iza
ti
o
n
fra
m
e
wo
rk
a
n
d
is
e
x
p
re
ss
e
d
th
r
o
u
g
h
li
n
e
a
r
m
a
tri
x
in
e
q
u
a
li
t
y
c
o
n
str
a
in
ts.
T
h
e
fil
ter
is
d
e
sig
n
e
d
t
o
p
ro
d
u
c
e
a
r
e
sid
u
a
l
si
g
n
a
l
th
a
t
b
a
lan
c
e
s
two
o
p
p
o
si
n
g
o
b
jec
ti
v
e
s:
m
in
imiz
in
g
th
e
imp
a
c
t
o
f
d
istu
r
b
a
n
c
e
s
a
n
d
m
o
d
e
l
u
n
c
e
rtain
ti
e
s
wh
il
e
m
a
x
imiz
in
g
fa
u
lt
se
n
sit
i
v
it
y
.
Th
e
e
ffe
c
ti
v
e
n
e
ss
o
f
t
h
e
p
ro
p
o
se
d
m
e
th
o
d
is
d
e
m
o
n
stra
te
d
th
ro
u
g
h
sim
u
latio
n
s
in
v
o
lv
i
n
g
se
n
so
r
a
n
d
a
c
tu
a
to
r
fa
u
lt
d
e
t
e
c
ti
o
n
in
th
e
we
ll
-
k
n
o
wn
th
re
e
-
tan
k
s
y
ste
m
.
S
imu
lati
o
n
re
su
lt
s
il
lu
stra
te t
h
e
m
e
th
o
d
'
s a
b
il
it
y
t
o
m
a
in
tain
ro
b
u
st
n
e
ss
a
g
a
in
st d
ist
u
r
b
a
n
c
e
s a
n
d
u
n
c
e
rtain
ti
e
s wh
il
e
e
ffe
c
ti
v
e
ly
d
e
t
e
c
ti
n
g
fa
u
l
ts i
n
th
e
sy
ste
m
.
K
ey
w
o
r
d
s
:
Fau
lt d
etec
tio
n
L
in
ea
r
m
atr
ix
in
eq
u
ality
Mo
d
el
u
n
ce
r
tain
ty
Ob
s
er
v
er
d
esig
n
R
o
b
u
s
tn
ess
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
R
o
s
m
iwati
Mo
h
d
-
Mo
k
h
tar
Sch
o
o
l o
f
E
lectr
ical
a
n
d
E
lectr
o
n
ic
E
n
g
i
n
ee
r
in
g
,
E
n
g
i
n
ee
r
in
g
C
am
p
u
s
,
Un
iv
er
s
iti Sain
s
Ma
lay
s
ia
Pen
an
g
,
Ma
lay
s
ia
E
m
ail:
ee
r
o
s
m
iwati@
u
s
m
.
m
y
1.
I
NT
RO
D
UCT
I
O
N
Fau
lt
d
etec
tio
n
is
ess
en
tial
in
r
o
b
o
tics
an
d
a
u
to
m
atio
n
s
y
s
tem
s
to
en
s
u
r
e
r
eliab
ili
ty
,
s
af
ety
,
en
v
ir
o
n
m
en
tal
s
u
s
tain
ab
ilit
y
,
an
d
ac
h
ie
v
e
d
esire
d
p
er
f
o
r
m
a
n
ce
lev
els
[
1
]
.
I
t
i
d
en
tifie
s
is
s
u
es
ea
r
ly
,
m
i
n
im
izes
d
o
wn
tim
e,
p
r
ev
e
n
ts
ac
cid
en
t
s
,
an
d
m
ain
tain
s
p
r
o
d
u
ct
q
u
ality
.
I
n
th
e
in
d
u
s
tr
y
,
it
in
cr
ea
s
es
p
r
o
d
u
ctiv
ity
,
en
s
u
r
es
o
p
er
atio
n
al
co
n
tin
u
ity
,
an
d
co
n
tr
i
b
u
tes
to
s
u
s
tain
ab
ilit
y
b
y
p
r
ev
e
n
tin
g
waste
an
d
in
ef
f
icien
cies.
R
o
b
o
tics
an
d
au
to
m
atio
n
s
y
s
tem
s
f
r
eq
u
en
tly
in
ter
ac
t
with
h
u
m
an
s
o
r
h
az
ar
d
o
u
s
m
ater
ia
ls
.
Dete
ctin
g
f
au
lt
s
ea
r
ly
p
r
ev
en
ts
ac
cid
e
n
ts
,
p
r
o
t
ec
ts
wo
r
k
er
s
,
a
n
d
m
in
im
izes
r
is
k
s
.
As
in
d
u
s
tr
ies
ad
o
p
t
s
m
ar
t
m
an
u
f
ac
tu
r
in
g
,
f
au
lt
d
etec
tio
n
b
ec
o
m
es
in
teg
r
al
to
r
ea
l
-
tim
e
m
o
n
ito
r
in
g
,
s
elf
-
d
iag
n
o
s
is
,
an
d
au
to
n
o
m
o
u
s
d
ec
is
io
n
-
m
ak
in
g
,
k
ey
p
r
in
ci
p
les
o
f
I
n
d
u
s
tr
y
4
.
0
.
Me
etin
g
th
ese
r
eq
u
ir
em
e
n
ts
o
f
ten
in
cr
ea
s
es
b
o
th
s
y
s
tem
c
o
m
p
lex
ity
an
d
co
s
t.
Fau
lts
o
r
ab
n
o
r
m
al
b
eh
a
v
io
r
s
in
s
u
ch
co
m
p
lex
s
y
s
tem
s
ca
n
d
eg
r
a
d
e
p
e
r
f
o
r
m
an
ce
a
n
d
p
o
ten
tially
lead
to
h
az
ar
d
o
u
s
s
itu
atio
n
s
,
p
o
s
in
g
r
i
s
k
s
to
h
u
m
an
s
af
ety
a
n
d
f
in
a
n
cial
lo
s
s
.
T
h
u
s
,
ea
r
ly
d
etec
tio
n
an
d
id
e
n
tific
atio
n
o
f
ab
n
o
r
m
al
s
y
s
tem
b
eh
a
v
io
r
s
ar
e
ess
en
tial
to
p
r
ev
en
t
th
e
s
e
ad
v
er
s
e
o
u
tco
m
es
[
2
]
–
[
5
]
.
Ov
er
th
e
p
ast
two
d
ec
ad
es,
n
u
m
er
o
u
s
ad
v
a
n
ce
m
en
ts
in
r
esil
ien
t
f
au
lt
d
etec
tio
n
(
FD)
s
y
s
tem
d
esig
n
h
av
e
b
ee
n
m
ad
e,
b
r
o
ad
ly
ca
teg
o
r
ized
in
to
m
o
d
el
-
b
ased
an
d
m
o
d
el
-
f
r
ee
ap
p
r
o
ac
h
es
[
6
]
–
[
9
]
.
Am
o
n
g
m
o
d
el
-
b
ased
m
eth
o
d
s
,
o
b
s
er
v
e
r
-
b
ased
tech
n
iq
u
es h
av
e
g
ain
e
d
p
o
p
u
lar
ity
d
u
e
to
th
eir
s
im
p
ler
s
tr
u
ctu
r
e
an
d
r
elativ
ely
lo
wer
d
esig
n
co
m
p
lex
ity
[
1
0
]
,
[
1
1
]
.
T
h
ese
a
p
p
r
o
ac
h
es
u
tili
ze
a
f
au
lt
d
etec
tio
n
f
ilter
(
FDF)
to
g
en
er
ate
a
r
esid
u
al,
d
ef
in
e
d
as
th
e
d
if
f
er
en
ce
b
etwe
en
th
e
s
y
s
te
m
'
s
m
ea
s
u
r
ed
o
u
tp
u
ts
an
d
th
e
esti
m
ated
o
u
tp
u
ts
d
er
iv
e
d
f
r
o
m
its
m
o
d
el.
B
y
co
m
p
ar
in
g
th
e
r
esid
u
al
a
g
ain
s
t a
p
r
ed
e
f
in
ed
th
r
esh
o
ld
,
t
h
e
o
c
cu
r
r
en
ce
o
f
f
a
u
lts
ca
n
b
e
id
e
n
tifie
d
[
1
2
]
,
[
1
3
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
Desig
n
o
f H
-
/H∞ b
a
s
ed
fa
u
lt
d
etec
tio
n
filt
er fo
r
lin
ea
r
u
n
ce
r
ta
in
s
ystem
s
…
(
Ma
s
o
o
d
A
h
m
a
d
)
215
T
h
e
p
r
esen
ce
o
f
ex
ter
n
al
d
is
tu
r
b
an
ce
s
an
d
m
o
d
el
u
n
ce
r
tai
n
ties
co
m
p
licates
th
e
r
es
id
u
al
g
en
er
atio
n
p
r
o
ce
s
s
,
o
f
ten
p
r
o
d
u
cin
g
n
o
n
-
ze
r
o
r
esid
u
als
ev
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n
in
f
a
u
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f
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ee
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ce
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s
.
I
d
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lly
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a
f
a
u
lt
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f
r
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tem
s
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o
u
ld
y
ield
a
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v
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esid
u
al,
wh
ile
f
au
lty
co
n
d
itio
n
s
s
h
o
u
ld
r
esu
lt
in
a
n
o
n
-
ze
r
o
r
esid
u
al.
Ho
wev
er
,
d
is
tu
r
b
an
ce
s
an
d
u
n
ce
r
tain
ties
m
ay
lead
t
o
f
alse
alar
m
s
,
u
n
d
er
m
i
n
in
g
t
h
e
FD
p
r
o
ce
s
s
.
T
h
er
ef
o
r
e,
r
o
b
u
s
t
r
esid
u
al
g
en
er
atio
n
is
cr
itical
f
o
r
ef
f
ec
tiv
e
FD
[
1
4
]
–
[
1
7
]
.
A
d
d
r
ess
in
g
d
is
tu
r
b
a
n
ce
s
an
d
m
o
d
el
u
n
ce
r
tain
ty
i
n
m
o
d
el
-
b
ased
FD
s
y
s
tem
s
p
r
es
en
ts
a
s
ig
n
if
ican
t
ch
allen
g
e.
T
o
th
is
en
d
,
th
e
H∞
n
o
r
m
o
p
ti
m
izatio
n
tech
n
iq
u
e
h
as
b
ee
n
em
p
l
o
y
ed
to
en
h
a
n
ce
r
esid
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al
r
o
b
u
s
tn
ess
ag
ain
s
t
d
i
s
tu
r
b
an
ce
s
[
1
8
]
.
C
o
n
v
er
s
ely
,
t
h
e
H
-
in
d
ex
,
wh
ic
h
r
ef
lects th
e
m
in
im
u
m
f
au
lt sen
s
itiv
ity
o
f
th
e
r
esid
u
al,
h
as b
ee
n
u
s
ed
to
d
esig
n
f
a
u
lt
-
s
en
s
itiv
e
FDFs
,
en
h
an
cin
g
th
eir
s
en
s
itiv
ity
to
f
au
lts
[
1
9
]
–
[
2
1
]
.
W
h
ile
H∞
o
p
tim
izatio
n
en
s
u
r
es
r
o
b
u
s
tn
ess
ag
ain
s
t
d
is
tu
r
b
an
ce
s
,
it
also
r
ed
u
ce
s
f
au
lt
s
en
s
itiv
ity
,
an
d
s
im
ilar
ly
,
H
-
in
d
ex
-
b
ased
F
DFs
,
alth
o
u
g
h
f
au
lt
-
s
en
s
itiv
e,
m
ay
am
p
lify
th
e
in
f
lu
en
ce
o
f
d
is
tu
r
b
a
n
ce
s
[
2
2
]
.
B
alan
cin
g
th
ese
tr
ad
e
-
o
f
f
s
is
k
ey
to
ac
h
iev
in
g
o
p
tim
al
FD p
er
f
o
r
m
a
n
ce
.
An
o
p
tim
al
FD
s
y
s
tem
aim
s
t
o
m
in
im
ize
th
e
im
p
ac
t
o
f
u
n
k
n
o
wn
d
is
tu
r
b
a
n
ce
s
(
m
in
im
izi
n
g
th
e
H∞
n
o
r
m
)
wh
ile
m
ax
im
izin
g
f
a
u
lt
s
en
s
itiv
ity
(
m
ax
im
izin
g
t
h
e
H
-
in
d
ex
)
,
f
r
a
m
in
g
t
h
e
d
esig
n
as
a
m
u
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
p
r
o
b
lem
.
A
liter
atu
r
e
r
e
v
iew
in
d
icate
s
th
at
m
o
s
t
FD
m
eth
o
d
s
a
d
d
r
ess
r
o
b
u
s
t
n
ess
an
d
s
en
s
itiv
ity
is
s
u
es
f
o
r
co
n
tin
u
o
u
s
-
tim
e
o
r
d
is
cr
ete
-
tim
e
lin
ea
r
s
y
s
te
m
s
with
ex
ter
n
al
d
is
tu
r
b
a
n
c
es
o
n
ly
[
2
3
]
–
[
2
6
]
.
Ho
wev
er
,
m
o
d
el
u
n
ce
r
tain
ties
in
s
y
s
tem
m
atr
ices
ca
n
in
tr
o
d
u
ce
b
iases
in
th
e
r
esid
u
al,
n
ec
ess
itatin
g
ca
r
ef
u
l
h
an
d
lin
g
t
o
en
s
u
r
e
r
o
b
u
s
t
r
esid
u
al
g
en
er
atio
n
.
Fo
r
u
n
ce
r
ta
in
co
n
tin
u
o
u
s
-
tim
e
lin
ea
r
s
y
s
tem
s
,
an
o
b
s
er
v
er
-
b
ased
FD
s
y
s
tem
was
p
r
o
p
o
s
ed
in
[
2
7
]
,
u
tili
zin
g
iter
ativ
e
lin
ea
r
m
atr
ix
in
eq
u
alities
(
L
MI
s
)
to
g
en
er
ate
r
o
b
u
s
t
r
esid
u
als.
T
h
is
ap
p
r
o
ac
h
p
r
o
v
i
d
ed
an
o
p
tim
al
b
alan
ce
b
etwe
en
r
o
b
u
s
tn
ess
to
d
is
tu
r
b
a
n
ce
s
an
d
f
a
u
lt
s
en
s
itiv
ity
f
o
r
th
e
m
u
lti
-
o
b
jectiv
e
o
p
tim
i
za
tio
n
p
r
o
b
le
m
.
Ho
wev
er
,
th
e
m
eth
o
d
'
s
co
m
p
lex
ity
in
cr
ea
s
ed
d
u
e
to
th
e
n
ee
d
to
f
ir
s
t
d
er
iv
e
a
th
eo
r
etica
lly
o
p
t
im
al
s
o
lu
tio
n
an
d
s
u
b
s
eq
u
en
tl
y
d
esig
n
th
e
o
b
s
er
v
er
.
I
n
c
o
n
t
r
ast,
an
H∞
b
ased
FD
r
esid
u
al
g
e
n
er
ato
r
f
o
r
lin
ea
r
s
y
s
tem
s
was
d
ev
elo
p
ed
in
[
2
8
]
,
d
em
o
n
s
tr
atin
g
r
o
b
u
s
tn
ess
ag
ain
s
t
d
is
tu
r
b
an
ce
s
an
d
m
o
d
el
u
n
ce
r
tain
ty
.
Nev
er
th
eless
,
th
is
ap
p
r
o
ac
h
d
id
n
o
t
ad
d
r
ess
f
au
lt
s
en
s
itiv
ity
is
s
u
e
s
.
Fo
r
s
u
cc
ess
f
u
l FD,
it is
cr
u
cial
to
s
im
u
ltan
eo
u
s
ly
co
n
s
id
er
f
au
lt s
en
s
itiv
ity
an
d
r
o
b
u
s
tn
ess
.
Mo
tiv
ated
b
y
th
e
s
ca
r
city
o
f
s
o
lu
tio
n
s
ad
d
r
ess
in
g
th
e
m
u
lti
-
o
b
jectiv
e
o
p
tim
izatio
n
p
r
o
b
lem
f
o
r
d
is
cr
ete
-
tim
e
lin
ea
r
s
y
s
tem
s
with
n
o
r
m
-
b
o
u
n
d
ed
m
o
d
el
u
n
ce
r
tain
ties
,
th
is
s
tu
d
y
s
ee
k
s
to
d
ev
elo
p
a
n
o
p
tim
al
o
b
s
er
v
er
-
b
ased
r
esid
u
al
g
e
n
er
ato
r
.
T
h
e
p
r
o
p
o
s
ed
m
et
h
o
d
en
s
u
r
es
o
b
s
er
v
er
s
tab
ilit
y
wh
ile
ac
h
iev
in
g
r
o
b
u
s
tn
ess
to
d
is
tu
r
b
an
ce
s
,
r
esil
ien
ce
ag
ain
s
t
m
o
d
el
u
n
c
er
tain
ties
,
an
d
en
h
an
ce
d
f
au
lt
s
en
s
itiv
ity
.
T
h
e
ex
is
ten
ce
o
f
th
e
p
r
o
p
o
s
ed
o
b
s
er
v
er
is
estab
lis
h
ed
th
r
o
u
g
h
s
u
f
f
icien
t
co
n
d
itio
n
s
ex
p
r
e
s
s
ed
as
L
MI
s
.
T
h
e
r
esu
lts
o
b
tain
ed
f
o
r
th
e
o
b
s
er
v
er
-
b
ased
f
au
lt d
etec
tio
n
f
ilter
wer
e
illu
s
tr
ated
th
r
o
u
g
h
a
s
im
u
latio
n
an
aly
s
is
o
f
a
th
r
ee
-
tan
k
s
y
s
tem
.
T
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
ca
n
b
e
ap
p
lied
to
an
y
d
is
cr
ete
-
tim
e
lin
ea
r
s
y
s
tem
with
n
o
r
m
-
b
o
u
n
d
ed
m
o
d
el
u
n
ce
r
tain
ties
an
d
d
is
tu
r
b
a
n
ce
s
.
T
h
e
k
ey
co
n
t
r
ib
u
tio
n
s
o
f
th
is
r
esear
ch
ar
e
o
u
tlin
ed
as f
o
llo
ws:
a.
Dev
elo
p
m
en
t
o
f
an
H∞ o
b
s
er
v
er
-
b
ased
f
ilter
to
m
in
im
ize
th
e
H∞ n
o
r
m
o
f
G
rd
,
th
e
tr
an
s
f
e
r
f
u
n
ctio
n
m
atr
ix
r
ep
r
esen
tin
g
th
e
d
is
tu
r
b
an
c
e
-
to
-
r
esid
u
al
r
elatio
n
s
h
i
p
,
with
in
th
e
lin
ea
r
m
atr
ix
in
eq
u
ality
(
L
M
I
)
f
r
am
ewo
r
k
.
b.
Dev
elo
p
m
en
t
o
f
an
H
-
o
b
s
er
v
er
-
b
ased
f
ilter
aim
ed
at
m
a
x
im
izin
g
th
e
H
-
n
o
r
m
o
f
G
rf
,
th
e
tr
an
s
f
er
f
u
n
ctio
n
m
atr
ix
f
r
o
m
f
au
lt to
r
esid
u
al,
a
ls
o
u
s
in
g
th
e
L
MI
f
r
am
ewo
r
k
.
c.
Desig
n
o
f
an
o
b
s
er
v
e
r
-
b
ase
d
f
ilter
u
tili
zin
g
th
e
H
-
/H∞
o
p
tim
izatio
n
m
eth
o
d
,
wh
ic
h
co
n
cu
r
r
e
n
tly
m
in
im
izes
th
e
H∞
n
o
r
m
wh
ile
m
ax
im
izin
g
th
e
H
-
n
o
r
m
.
T
h
is
ap
p
r
o
ac
h
s
ee
k
s
to
cr
e
ate
an
o
p
tim
al
o
b
s
er
v
er
-
b
ased
r
esid
u
al
g
e
n
er
ato
r
th
at
s
atis
f
ies b
o
th
H∞ a
n
d
H
-
p
er
f
o
r
m
an
ce
cr
iter
ia.
d.
Af
ter
co
n
s
tr
u
ctin
g
th
e
p
r
o
p
o
s
ed
o
b
s
er
v
er
,
th
e
l
2
n
o
r
m
is
ap
p
lied
to
ass
ess
an
d
co
m
p
ar
e
th
e
g
en
er
ated
r
esid
u
al
ag
ain
s
t a
d
ef
in
e
d
th
r
e
s
h
o
ld
to
d
etec
t f
a
u
lts
.
T
h
e
s
tr
u
ctu
r
e
o
f
th
e
p
ap
e
r
is
as
f
o
llo
ws
.
Sectio
n
2
in
tr
o
d
u
ce
s
th
e
p
r
o
b
lem
f
o
r
m
u
latio
n
.
Sectio
n
3
d
etails
th
e
co
r
e
co
n
tr
ib
u
tio
n
o
f
th
e
r
esear
ch
,
in
cl
u
d
in
g
th
e
d
er
iv
atio
n
o
f
th
e
f
ilter
g
ai
n
m
atr
ix
.
Sectio
n
4
p
r
o
v
id
es
s
im
u
latio
n
r
esu
lts
s
h
o
wca
s
in
g
th
e
f
ilter
'
s
ef
f
ec
tiv
en
ess
,
p
ar
ticu
lar
ly
in
d
etec
tin
g
s
en
s
o
r
an
d
ac
tu
ato
r
f
au
lts
with
in
a
th
r
ee
-
tan
k
s
y
s
tem
.
Fin
ally
,
s
ec
tio
n
5
p
r
esen
ts
co
n
clu
d
in
g
r
em
a
r
k
s
.
2.
P
RO
B
L
E
M
F
O
R
M
U
L
AT
I
O
N
T
h
e
d
is
cr
ete
-
tim
e
lin
ea
r
s
y
s
te
m
in
(
1
)
is
ad
o
p
ted
to
f
o
r
m
u
lat
e
th
e
p
r
o
b
lem
b
ein
g
s
o
lv
ed
in
th
is
p
ap
er
.
(
+
1
)
=
(
)
+
(
)
+
(
)
+
(
+
)
(
)
+
(
)
(
)
=
(
)
+
(
)
+
(
)
+
(
+
)
(
)
+
(
)
(
1
)
L
et
x
(
k
)
∈
R
n
r
e
p
r
esen
t
th
e
s
tate
v
ec
to
r
,
u
(
k
)
∈
R
p
th
e
c
o
n
t
r
o
l
in
p
u
t
v
ec
t
o
r
,
an
d
y
(
k
)
∈
R
m
th
e
m
ea
s
u
r
e
m
en
t
v
ec
to
r
.
T
h
e
d
is
tu
r
b
an
ce
v
ec
t
o
r
d
(
k
)
is
l
2
n
o
r
m
b
o
u
n
d
e
d
,
s
u
ch
th
at
∥
d
(
k
)
∥
2
≤
δ
d
,
wh
ile
f
(
k
)
is
t
h
e
l
2
n
o
r
m
b
o
u
n
d
ed
f
au
lt
v
ec
t
o
r
to
b
e
d
et
ec
ted
.
T
h
e
m
atr
ices
E
d
,
F
d
,
E
f
,
an
d
F
f
d
ef
in
e
th
e
lo
ca
tio
n
s
wh
er
e
th
e
d
is
tu
r
b
an
ce
an
d
f
a
u
lt
v
ec
to
r
s
in
f
lu
en
ce
th
e
s
y
s
tem
d
y
n
am
ics,
r
esp
ec
tiv
ely
.
T
h
e
m
atr
ices
A
,
B
,
C
,
an
d
D
ar
e
th
e
n
o
m
in
al
s
y
s
tem
m
atr
ices
wi
th
co
m
p
a
tib
le
d
im
en
s
io
n
s
,
an
d
ΔA
,
ΔB
,
ΔC
,
an
d
ΔD
r
ep
r
esen
t
n
o
r
m
-
b
o
u
n
d
e
d
m
o
d
el
u
n
ce
r
tain
ties
,
g
iv
en
as (
2
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
14
,
No
.
2
,
J
u
n
e
20
2
5
:
214
-
2
2
6
216
[
∆
∆
∆
∆
]
=
[
1
∑
1
1
∑
2
2
∑
1
2
∑
2
]
(
2
)
wh
er
e
∑
is
an
u
n
k
n
o
wn
s
ca
lar
co
n
s
tan
t
h
o
l
d
s
th
e
c
o
n
d
itio
n
,
i
.
e.
,
∑
∑
≤
.
T
h
e
ass
u
m
p
tio
n
s
lis
ted
b
elo
w
ar
e
u
s
ed
co
n
s
is
ten
tly
th
r
o
u
g
h
o
u
t t
h
is
wo
r
k
[
1
8
]
:
A1
:
Sy
s
tem
(
1
)
is
o
b
s
er
v
ab
le
;
A2
:
[
−
]
h
as
f
u
ll
r
o
w
r
an
k
,
wh
i
le
∈
[
0
,
2
]
;
A3
:
(
+
)
is
s
tab
le
As
in
itially
in
tr
o
d
u
ce
d
,
t
h
e
m
o
d
el
-
b
ased
FD
s
y
s
tem
co
m
p
r
is
es
two
s
u
b
s
y
s
tem
s
:
a
r
esid
u
a
l
g
en
er
ato
r
an
d
a
r
esid
u
al
ev
alu
at
o
r
with
th
r
esh
o
ld
in
g
an
d
d
ec
is
io
n
lo
g
ic.
An
o
b
s
er
v
e
r
-
b
ased
FD
f
ilter
is
u
s
ed
f
o
r
g
en
er
atin
g
t
h
e
r
esid
u
al,
wh
ic
h
is
ex
p
r
ess
ed
as (
3
)
:
̂
(
+
1
)
=
̂
(
)
+
(
(
)
−
̂
(
)
)
+
(
)
(
)
=
(
)
−
̂
(
)
(
3
)
(
̂
(
)
=
̂
(
)
+
(
)
)
∈
an
d
̂
(
)
∈
r
ep
r
esen
t
th
e
esti
m
ate
d
o
u
tp
u
t
a
n
d
th
e
s
tate
esti
m
atio
n
v
ec
to
r
s
,
r
esp
ec
tiv
ely
.
T
h
e
r
e
s
id
u
al
s
ig
n
al
is
d
en
o
ted
b
y
(
)
,
an
d
th
e
f
ilter
g
ain
s
er
v
es
a
s
th
e
d
esig
n
p
ar
am
eter
f
o
r
th
e
p
r
o
p
o
s
ed
F
D
f
ilter
.
T
h
e
d
y
n
am
ics
o
f
th
e
f
ilter
ar
e
d
escr
ib
ed
b
y
th
e
s
tate
esti
m
atio
n
er
r
o
r
v
ec
to
r
,
(
)
=
(
)
−
̂
(
)
.
T
h
e
f
o
llo
win
g
eq
u
atio
n
s
r
ep
r
esen
t th
e
er
r
o
r
d
y
n
am
i
cs a
n
d
th
e
r
esid
u
al:
(
+
1
)
=
(
−
)
(
)
+
(
−
)
(
)
+
(
−
)
(
)
+
(
−
)
(
)
+
(
−
)
(
)
(
4
)
(
)
=
(
)
+
(
)
+
(
)
+
(
)
+
(
)
(
5
)
Un
d
esire
d
b
eh
a
v
io
r
in
FD
th
e
o
r
y
is
ca
u
s
ed
b
y
m
o
d
el
u
n
ce
r
tain
ty
an
d
d
is
tu
r
b
an
ce
,
w
h
ich
i
n
f
lu
en
ce
s
th
e
esti
m
atio
n
p
r
o
ce
s
s
an
d
m
ak
es
th
e
r
esid
u
al
s
en
s
itiv
e
to
f
au
lts
,
co
n
tr
o
l
i
n
p
u
t,
an
d
t
h
e
s
y
s
tem
'
s
s
tate
[
2
9
]
.
Fo
r
th
e
s
ak
e
o
f
s
im
p
licity
,
th
e
d
y
n
am
ics o
f
(
4
)
ar
e
g
o
v
er
n
ed
b
y
two
n
ew
v
ec
to
r
s
:
̅
(
)
=
[
(
)
(
)
]
an
d
̅
(
)
=
[
(
)
(
)
]
T
h
en
,
an
au
g
m
e
n
ted
s
y
s
tem
is
r
ep
r
esen
ted
as
(
6
)
,
(
7
)
:
̅
(
+
1
)
=
̅
̅
(
)
+
̅
̅
(
)
+
̅
(
)
(
6
)
(
)
=
̅
̅
(
)
+
̅
̅
(
)
+
(
)
(
7
)
wh
er
e
̅
=
[
−
−
0
+
]
;
̅
=
[
−
−
+
]
;
̅
=
[
]
;
̅
=
[
]
;
̅
=
[
−
]
T
h
e
r
esid
u
al
s
ig
n
al
in
(
7
)
ca
n
b
e
r
ep
r
esen
ted
in
th
e
f
r
eq
u
e
n
c
y
d
o
m
ai
n
.
(
)
=
̅
(
)
̅
(
)
+
(
)
(
)
(
8
)
wh
er
e
̅
(
)
=
̅
(
−
̅
+
̅
)
−
1
(
̅
−
̅
)
+
̅
an
d
(
)
=
̅
(
−
̅
+
̅
)
−
1
(
̅
−
)
+
̅
(
)
an
d
(
)
ar
e
th
e
tr
an
s
f
er
f
u
n
ctio
n
m
atr
ices f
r
o
m
̅
(
)
an
d
(
)
to
(
)
,
r
esp
ec
tiv
ely
.
T
h
e
in
f
l
u
en
ce
o
f
d
is
tu
r
b
a
n
ce
an
d
m
o
d
el
u
n
ce
r
tain
ty
o
n
t
h
e
r
esid
u
al
is
m
ea
s
u
r
ed
b
y
∞
n
o
r
m
a
n
d
is
r
ep
r
esen
ted
as
(
9
)
:
∞
=
‖
̅
(
)
‖
∞
=
s
up
∈
[
0
,
2
]
̅
(
̅
(
)
)
=
s
up
̅
(
)
∈
2
,
‖
̅
‖
2
≠
0
{
∑
(
)
(
)
∞
=
0
∑
̅
(
)
̅
(
)
∞
=
0
}
(
9
)
R
o
b
u
s
tn
ess
ag
ain
s
t d
is
tu
r
b
an
ce
an
d
m
o
d
el
u
n
ce
r
tain
ty
is
ex
p
r
ess
ed
b
y
(
1
0
)
[
3
0
]
.
‖
̅
(
)
‖
∞
<
;
>
0
(
1
0
)
r
ep
r
esen
ts
th
e
m
ax
im
u
m
e
f
f
e
ct
o
f
m
o
d
el
u
n
ce
r
tain
ty
a
n
d
d
is
tu
r
b
an
ce
o
n
th
e
r
esid
u
al,
an
d
th
e
v
alu
e
o
f
s
h
o
u
ld
b
e
s
m
aller
.
L
ik
ewise,
th
e
ef
f
ec
t o
f
f
au
lt
o
n
th
e
r
esid
u
al
is
ch
ar
ac
ter
ized
b
y
−
in
d
ex
[
3
1
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
Desig
n
o
f H
-
/H∞ b
a
s
ed
fa
u
lt
d
etec
tio
n
filt
er fo
r
lin
ea
r
u
n
ce
r
ta
in
s
ystem
s
…
(
Ma
s
o
o
d
A
h
m
a
d
)
217
−
=
‖
(
)
‖
−
=
in
f
∈
[
0
,
2
]
[
(
)
]
(
1
1
)
T
h
e
r
esid
u
al'
s
s
en
s
itiv
ity
to
th
e
f
au
lt is
illu
s
tr
ated
b
y
(
1
2
)
.
‖
(
)
‖
−
>
;
>
0
(
1
2
)
d
en
o
tes
th
e
wo
r
s
t
-
ca
s
e
f
au
lt
s
en
s
itiv
ity
m
ea
s
u
r
em
en
t
o
f
th
e
r
esid
u
al
s
ig
n
al.
A
lar
g
er
v
alu
e
o
f
s
h
o
ws
th
at
r
esid
u
al
is
m
o
r
e
s
en
s
itiv
e
to
a
f
au
lt.
T
h
e
s
o
lu
tio
n
o
f
an
o
p
tim
al
FD
f
ilter
d
esig
n
b
ased
o
n
−
∞
o
p
tim
izatio
n
f
o
r
th
e
n
o
m
in
al
s
y
s
tem
(
s
y
s
tem
u
n
ce
r
tain
ty
,
=
0
)
ca
n
b
e
ea
s
ily
o
b
tain
ed
b
y
s
o
lv
i
n
g
a
s
in
g
le
R
icca
ti
eq
u
atio
n
[
1
8
]
.
Un
f
o
r
tu
n
ately
,
th
e
R
icca
ti
eq
u
atio
n
ca
n
n
o
t
s
o
lv
e
−
∞
o
p
tim
izatio
n
p
r
o
b
lem
s
f
o
r
d
y
n
am
ic
s
y
s
tem
s
with
m
o
d
el
u
n
ce
r
tain
ties
(
≠
0
)
.
T
h
e
m
u
lti
-
o
b
jectiv
e
o
p
tim
iz
atio
n
p
r
o
b
lem
f
o
r
lin
ea
r
s
y
s
t
em
s
s
u
b
ject
to
d
is
tu
r
b
a
n
ce
a
n
d
m
o
d
el
u
n
ce
r
tain
ty
is
ad
d
r
ess
ed
in
th
is
s
tu
d
y
u
s
in
g
th
e
L
MI
tech
n
iq
u
e.
Usi
n
g
−
∞
o
p
tim
izatio
n
,
th
e
o
b
jectiv
e
is
to
d
esig
n
an
o
p
tim
al
FD
f
ilter
b
y
d
eter
m
in
in
g
th
e
f
ilter
g
ain
m
atr
ix
in
a
way
th
at
(
a
)
m
ak
es
th
e
au
g
m
en
te
d
s
y
s
tem
(
6
)
asy
m
p
to
tically
s
ta
b
le,
(
b
)
m
ak
es
th
e
r
esid
u
al
(
7
)
r
o
b
u
s
t
to
d
is
tu
r
b
an
ce
an
d
m
o
d
el
u
n
ce
r
tain
ties
in
th
e
∞
s
en
s
e,
an
d
(
c
)
m
ak
es th
e
r
esid
u
al
(
7
)
f
a
u
lt
-
s
en
s
itiv
e.
3.
SYNT
H
E
S
I
S O
F
O
P
T
I
M
AL
F
D
F
I
L
T
E
R
I
n
th
is
s
ec
tio
n
,
an
o
p
tim
al
FD
f
ilter
is
d
esig
n
ed
f
o
r
s
y
s
tem
(
1
)
in
th
e
L
MI
f
r
a
m
ewo
r
k
.
First,
s
ep
ar
ate
s
o
lu
tio
n
s
o
f
∞
an
d
−
in
d
ex
co
n
d
itio
n
s
in
(
1
0
)
an
d
(
1
2
)
ar
e
o
b
tain
ed
,
f
o
llo
wed
b
y
an
alg
o
r
ith
m
f
o
r
s
o
lv
in
g
m
ix
ed
−
∞
o
p
tim
izatio
n
p
r
o
b
lem
.
Fo
r
o
n
war
d
d
is
cu
s
s
io
n
,
th
e
f
o
llo
win
g
lem
m
as
h
elp
to
d
er
iv
e
th
e
m
ain
r
esu
lts
.
L
em
m
a
1
[
1
8
]
:
T
h
e
o
b
s
er
v
er
er
r
o
r
d
y
n
am
ics
(
4
)
is
asy
m
p
t
o
tically
s
tab
le
an
d
m
ee
ts
th
e
c
o
n
d
itio
n
(
1
0
)
f
o
r
t
h
e
lin
ea
r
s
y
s
tem
(
1
)
with
ze
r
o
m
o
d
el
u
n
ce
r
tain
ty
in
th
e
s
y
s
tem
m
atr
ices
if
th
e
f
o
llo
win
g
L
M
I
is
tr
u
e
f
o
r
(
(
)
=
0
)
th
en
th
er
e
e
x
is
ts
a
s
ca
lar
≥
m
i
n
,
m
atr
ix
an
d
=
>
0
.
[
−
(
−
)
(
−
)
0
(
−
)
−
0
(
−
)
0
−
0
−
]
<
0
T
h
e
ab
o
v
e
lem
m
a
p
r
o
v
i
d
es th
e
n
ec
ess
ar
y
an
d
s
u
f
f
icien
t c
o
n
d
itio
n
f
o
r
(
1
0
)
an
d
en
s
u
r
es th
a
t
‖
̅
(
)
‖
∞
<
.
L
em
m
a
2
[
1
8
]
:
T
h
e
o
b
s
er
v
er
er
r
o
r
d
y
n
am
ics
(
4
)
is
asy
m
p
t
o
tically
s
tab
le
an
d
m
ee
ts
th
e
c
o
n
d
itio
n
(
1
2
)
f
o
r
t
h
e
lin
ea
r
s
y
s
tem
(
1
)
with
ze
r
o
m
o
d
el
u
n
ce
r
tain
ty
i
n
th
e
s
y
s
tem
m
atr
ices
if
th
e
f
o
llo
win
g
L
MI
is
tr
u
e
f
o
r
(
̅
(
)
=
0
)
,
th
en
th
er
e
ex
is
ts
a
s
ca
lar
≤
m
ax
,
m
atr
ix
an
d
=
>
0
.
[
−
(
−
)
(
−
)
−
+
(
−
)
(
−
)
(
−
)
(
−
)
+
2
−
−
(
−
)
(
−
)
]
>
0
T
h
e
ab
o
v
e
lem
m
a
g
u
ar
a
n
tees
th
at
th
e
m
in
im
u
m
f
a
u
lt
s
en
s
itiv
ity
o
f
th
e
r
esid
u
al
is
g
r
ea
te
r
t
h
an
a
co
n
s
tan
t,
i.e
.
,
‖
(
)
‖
−
>
.
L
em
m
a
3
[
3
0
]
:
I
f
th
er
e
ex
is
ts
a
s
y
m
m
etr
ic
p
o
s
itiv
e
d
e
f
in
ite
m
atr
ix
,
an
d
an
ar
b
itra
r
y
p
o
s
itiv
e
s
ca
lar
>
0
th
at
s
atis
f
y
(
−
)
−
1
>
0
th
en
(
+
∑
)
(
+
∑
)
≤
+
(
−
)
−
1
+
L
em
m
a
4
[
3
2
]
:
T
h
e
f
o
llo
win
g
co
n
d
itio
n
s
ar
e
e
q
u
iv
alen
t
wh
en
th
e
Sch
u
r
c
o
m
p
lem
e
n
t
p
r
i
n
cip
le
is
ap
p
lied
to
s
ev
er
al
s
y
m
m
etr
ic
m
atr
ices
11
,
12
an
d
22
.
If
11
<
0
th
en
[
11
12
21
22
]
<
0
if
an
d
o
n
l
y
if
22
−
21
(
11
)
−
1
12
<
0
If
22
<
0
th
en
[
11
12
21
22
]
<
0
if
an
d
o
n
ly
if
11
−
12
(
22
)
−
1
21
<
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
14
,
No
.
2
,
J
u
n
e
20
2
5
:
214
-
2
2
6
218
T
h
eo
r
em
1
:
C
o
n
s
id
er
s
y
s
tem
(
1
)
with
m
o
d
el
u
n
ce
r
tain
ties
(
∆
,
∆
,
∆
,
∆
≠
0
)
,
u
n
d
er
th
e
ass
u
m
p
tio
n
s
A1
an
d
A2
,
if
th
er
e
ex
is
t
s
ca
lar
s
>
0
,
>
0
,
a
f
ilter
g
ain
m
atr
ix
,
a
s
y
m
m
etr
ic
m
atr
ix
>
0
an
d
a
s
ca
lar
>
0
s
u
ch
th
at
th
e
au
g
m
e
n
ted
s
y
s
tem
(
6
)
is
asy
m
p
to
tically
s
tab
le
an
d
th
e
f
o
llo
win
g
m
atr
ix
i
n
eq
u
alities
h
o
ld
,
th
en
co
n
d
itio
n
s
(
1
0
)
an
d
(
1
2
)
ar
e
s
atis
f
ied
.
[
2
2
+
3
3
−
2
0
+
3
0
2
0
+
3
0
0
2
+
0
3
0
0
+
0
0
+
1
1
−
0
0
+
0
0
+
1
2
0
2
+
0
3
0
0
+
0
0
+
2
1
0
0
+
0
0
+
2
2
−
2
]
<
0
(
1
3
)
[
−
2
2
−
3
3
+
2
̅
+
3
̅
2
+
3
̅
̅
2
+
̅
3
−
̅
̅
−
̅
̅
−
1
1
+
−
̅
−
̅
̅
2
+
̅
3
−
̅
−
̅
̅
−
−
̅
̅
+
2
]
>
0
(
1
4
)
I
n
ad
d
itio
n
to
s
o
lv
in
g
(
1
3
)
a
n
d
(
1
4
)
,
o
p
tim
al
f
ilter
g
ain
,
ca
n
b
e
d
eter
m
i
n
ed
b
y
s
o
lv
i
n
g
th
e
f
o
llo
win
g
o
p
tim
izatio
n
p
r
o
b
lem
:
m
ax
=
(
1
5
)
Pro
o
f
o
f
th
e
T
h
e
o
r
em
Fo
r
th
e
au
g
m
en
ted
s
y
s
tem
(
6
)
an
d
(
7
)
,
(
1
0
)
ca
n
b
e
e
x
p
r
ess
ed
as
(
1
6
)
:
‖
̅
‖
∞
<
↔
∑
[
(
)
(
)
−
2
̅
(
)
̅
(
)
]
∞
=
0
<
;
(
)
=
0
(
1
6
)
Def
in
in
g
a
L
y
ap
u
n
o
v
f
u
n
ctio
n
,
(
̅
(
)
)
=
̅
(
)
̅
(
)
>
0
wh
er
e
=
dia
g
[
1
,
2
]
>
0
.
Su
p
p
o
s
e
>
0
,
th
e
n
ec
ess
ar
y
s
tab
ilit
y
co
n
d
iti
o
n
lis
ted
b
elo
w
is
en
s
u
r
ed
.
∑
(
(
̅
(
+
1
)
)
−
(
̅
(
)
)
)
∞
=
0
<
0
(
1
7
)
T
h
e
co
n
tr
o
l o
b
jectiv
e
(
1
0
)
an
d
∞
FD f
ilter
s
tab
ilit
y
is
en
s
u
r
ed
b
y
co
m
b
in
in
g
(
1
6
)
an
d
(
1
7
)
,
w
h
ich
will y
ield
∑
[
(
)
(
)
+
(
̅
(
+
1
)
)
−
(
̅
(
)
)
−
2
̅
(
)
̅
(
)
]
∞
=
0
<
0
(
1
8
)
Fro
m
eq
u
atio
n
(
6
)
an
d
(
7
)
,
it is
ea
s
y
to
wr
ite
[
̅
(
)
̅
(
)
]
(
[
̅
̅
]
[
̅
̅
]
+
[
̅
̅
]
[
̅
̅
]
+
[
−
0
0
−
2
]
)
[
̅
(
)
̅
(
)
]
<
0
(
1
9
)
T
h
e
co
n
s
tan
t a
n
d
u
n
ce
r
tain
s
y
s
tem
m
atr
ices a
r
e
d
iv
id
ed
as f
o
llo
ws to
av
o
id
a
n
y
am
b
ig
u
ity
:
[
̅
̅
̅
̅
]
=
[
0
0
0
0
]
+
[
∆
̅
∆
̅
∆
̅
∆
̅
]
(
2
0
)
w
h
er
e
[
0
0
0
0
]
=
[
0
0
−
0
0
−
0
]
;
[
∆
̅
∆
̅
∆
̅
∆
̅
]
=
[
2
1
−
2
1
]
∑
[
0
1
2
0
]
=
[
2
3
]
∑
[
1
2
]
=
∑
R
ep
r
esen
tin
g
th
e
ab
o
v
e
m
atr
ic
es a
s
:
=
[
0
0
0
0
]
;
=
[
−
0
0
]
;
=
[
0
−
]
;
=
[
0
]
;
=
[
0
]
;
=
[
2
3
]
;
3
=
[
1
−
2
1
]
;
=
[
1
2
]
;
1
=
[
0
1
]
;
2
=
[
2
0
]
;
=
[
−
0
0
−
2
]
;
=
[
0
0
]
Ap
p
ly
in
g
L
e
m
m
a
3
o
n
(
1
9
)
u
s
in
g
(
2
0
)
tu
r
n
s
to
(
2
1
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
Desig
n
o
f H
-
/H∞ b
a
s
ed
fa
u
lt
d
etec
tio
n
filt
er fo
r
lin
ea
r
u
n
ce
r
ta
in
s
ystem
s
…
(
Ma
s
o
o
d
A
h
m
a
d
)
219
[
̅
(
)
̅
(
)
]
(
(
+
∑
)
(
+
∑
)
+
)
[
̅
(
)
̅
(
)
]
(
2
1
)
(
+
∑
)
(
+
∑
)
+
≤
+
(
−
)
−
1
+
+
(
2
2
)
Ap
p
ly
in
g
L
e
m
m
a
4
o
n
(
2
2
)
will y
ield
(
2
3
)
.
[
−
+
+
]
<
0
(
2
3
)
E
x
p
an
d
i
n
g
(
2
3
)
,
o
n
e
ca
n
wr
ite
as
(
2
4
)
.
[
2
2
+
3
3
−
2
0
+
3
0
2
0
+
3
0
0
2
+
0
3
0
0
+
0
0
+
1
1
−
0
0
+
0
0
+
1
2
0
2
+
0
3
0
0
+
0
0
+
2
1
0
0
+
0
0
+
2
2
−
2
]
<
0
(
2
4
)
R
ewr
itin
g
th
e
ab
o
v
e
m
atr
ix
in
eq
u
ality
as
(
2
5
)
.
[
2
3
0
0
0
1
0
0
2
]
[
0
0
0
0
0
0
]
[
2
0
0
3
0
0
0
1
2
]
−
[
0
0
0
0
0
0
2
]
<
0
(
2
5
)
Ap
p
ly
in
g
th
e
Sch
u
r
c
o
m
p
lem
e
n
t le
m
m
a
g
iv
e
n
b
elo
w,
(
2
5
)
ca
n
b
e
r
e
p
r
esen
ted
as
(
2
6
)
.
[
−
0
0
0
−
0
0
0
−
2
2
3
0
0
0
1
0
0
2
2
0
0
3
0
0
0
1
2
−
0
0
0
−
−
1
0
0
0
−
−
1
]
<
0
(
2
6
)
T
h
e
n
o
n
lin
ea
r
in
eq
u
ality
is
tr
an
s
f
o
r
m
ed
in
t
o
lin
ea
r
in
e
q
u
ality
f
o
r
m
b
y
p
e
r
f
o
r
m
in
g
m
atr
ix
eq
u
iv
alen
t
tr
an
s
f
o
r
m
atio
n
as
(
2
7
)
.
[
−
0
0
0
−
0
0
0
−
2
2
3
0
0
0
1
0
0
2
2
0
0
3
0
0
0
1
2
−
0
0
0
−
0
0
0
−
]
<
0
(
2
7
)
B
y
in
s
er
tin
g
th
e
3
,
0
,
0
,
0
,
0
,
1
,
2
an
d
m
atr
ic
es
in
th
e
ab
o
v
e
m
atr
i
x
,
wh
ich
co
m
p
letes
th
e
p
r
o
o
f
o
f
th
e
f
ir
s
t p
ar
t o
f
T
h
eo
r
em
1
.
Similar
ly
,
−
in
d
ex
-
b
ased
f
au
lt sen
s
itiv
ity
co
n
d
itio
n
(
1
2
)
ca
n
b
e
d
er
iv
ed
as
(
2
8
)
.
‖
‖
−
>
↔
∑
[
(
)
(
)
>
2
(
)
(
)
]
∞
=
0
;
̅
(
)
=
0
(
2
8
)
C
o
n
s
id
er
in
g
th
e
L
y
a
p
u
n
o
v
f
u
n
ctio
n
d
ef
i
n
ed
ea
r
lier
,
(
)
=
̅
(
)
̅
(
)
>
0
,
>
0
.
T
h
e
co
n
tr
o
l
o
b
jectiv
e
(
1
2
)
a
n
d
−
in
d
ex
f
ilter
s
tab
ilit
y
is
en
s
u
r
ed
b
y
(
2
9
)
.
∑
[
(
)
(
)
−
(
̅
(
+
1
)
)
+
(
̅
(
)
)
−
2
(
)
(
)
]
∞
=
0
>
0
(
2
9
)
Af
ter
m
ath
em
atica
l simp
lific
atio
n
,
o
n
e
ca
n
wr
ite
(
2
9
)
as
(
3
0
)
.
∑
[
(
)
(
)
−
2
(
)
(
)
−
(
̅
(
+
1
)
)
+
(
̅
(
)
)
]
∞
=
0
<
0
(
3
0
)
Su
b
s
titu
tin
g
m
atr
ices
f
r
o
m
(
6
)
an
d
(
7
)
in
to
(
3
0
)
b
y
tak
in
g
̅
(
)
=
0
,
ca
n
b
e
wr
itten
in
m
at
r
ix
f
o
r
m
as
(
3
1
)
an
d
(
3
2
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
14
,
No
.
2
,
J
u
n
e
20
2
5
:
214
-
2
2
6
220
[
̅
]
(
[
̅
̅
]
[
̅
̅
]
+
[
̅
]
[
̅
]
+
[
−
0
0
−
2
]
)
[
̅
]
<
0
(
3
1
)
[
̅
]
(
[
̅
̅
̅
]
[
0
0
]
[
̅
̅
̅
]
+
[
−
0
0
−
2
]
)
[
̅
]
<
0
(
3
2
)
T
h
e
co
n
s
tan
t a
n
d
u
n
ce
r
tain
m
a
tr
ices a
r
e
s
ep
ar
ated
as
:
[
̅
̅
̅
]
=
[
̅
̅
̅
]
+
[
∆
̅
∆
∆
̅
∆
̅
]
(
3
3
)
wh
er
e
[
̅
̅
̅
]
=
[
0
−
0
0
−
]
an
d
[
∆
̅
∆
∆
̅
∆
̅
]
=
[
2
1
−
2
1
]
∑
[
0
1
0
]
Def
in
in
g
th
e
n
ew
m
atr
ices:
̿
=
[
̅
̅
̅
]
;
̅
=
[
−
0
0
]
;
̅
=
[
−
]
;
=
;
̅
=
[
0
]
;
=
[
2
3
]
;
3
=
[
1
−
2
1
]
;
=
[
1
0
]
;
1
=
[
0
1
]
;
=
[
0
0
]
;
1
=
[
−
0
0
−
2
]
It
is
s
im
p
le
to
wr
ite
(
3
2
)
as
f
o
l
lo
ws
u
s
in
g
L
em
m
a
3:
[
̅
]
(
(
̿
+
∑
)
(
̿
+
∑
)
+
1
)
[
̅
]
<
0
(
3
4
)
̿
̿
+
̿
(
−
)
−
1
̿
+
+
1
<
0
(
3
5
)
Acc
o
r
d
in
g
t
o
−
in
d
ex
cr
iter
ia
(
‖
(
)
‖
−
>
0
)
,
th
e
ab
o
v
e
in
eq
u
ality
is
wr
itten
as:
−
̿
1
̿
−
̿
1
(
−
1
)
−
1
1
̿
−
−
1
>
0
(
3
6
)
B
y
ap
p
ly
in
g
L
em
m
a
4
,
(
3
6
)
b
ec
o
m
es
(
3
7
)
.
[
−
̿
̿
−
̿
̿
−
−
1
]
>
0
(
3
7
)
E
x
p
an
d
i
n
g
m
atr
i
x
in
eq
u
ality
(
3
7
)
[
−
2
2
−
3
3
+
2
̅
+
3
̅
2
+
3
̅
̅
2
+
̅
3
−
̅
̅
−
̅
̅
−
1
1
+
−
̅
−
̅
̅
2
+
̅
3
−
̅
−
̅
̅
−
−
̅
̅
+
2
]
>
0
(
3
8
)
T
h
is
co
n
clu
d
es
t
h
e
p
r
o
o
f
o
f
T
h
eo
r
em
1
'
s
s
ec
o
n
d
p
ar
t.
FD
f
i
lter
g
ain
ca
n
b
e
ca
lcu
lated
b
y
s
o
lv
in
g
t
h
e
L
MI
s
(
2
7
)
a
n
d
(
3
8
)
f
o
r
t
h
e
o
p
tim
izat
io
n
p
r
o
b
lem
(
1
5
)
.
=
1
−
1
1
(
3
9
)
3
.
1
.
Resid
ua
l
ev
a
lua
t
io
n a
nd
t
hr
esh
o
ld
I
n
th
e
s
ec
o
n
d
s
tep
o
f
th
e
FD
p
r
o
ce
s
s
,
th
e
g
en
er
ated
r
esid
u
a
l
is
ev
alu
ated
u
s
in
g
2
s
ig
n
al
n
o
r
m
an
d
f
u
r
th
er
c
o
m
p
a
r
ed
with
th
e
th
r
esh
o
ld
,
ℎ
>
0
.
T
h
e
r
esid
u
al
(
3
)
t
h
at
was
g
en
er
ated
u
s
in
g
th
e
p
r
o
p
o
s
ed
FD
f
ilter
ca
n
b
e
s
h
o
w
n
as
(
4
0
)
:
(
)
=
(
)
+
(
)
+
(
)
(
4
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
Desig
n
o
f H
-
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a
s
ed
fa
u
lt
d
etec
tio
n
filt
er fo
r
lin
ea
r
u
n
ce
r
ta
in
s
ystem
s
…
(
Ma
s
o
o
d
A
h
m
a
d
)
221
I
n
f
a
u
lt
-
f
r
ee
ca
s
e,
(
)
=
0
,
th
en
th
e
r
e
s
id
u
al
ev
alu
atio
n
f
u
n
ctio
n
b
ec
o
m
es
=
‖
(
)
+
(
)
‖
2
2
.
T
h
u
s
,
th
e
th
r
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n
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m
p
u
ted
as
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up
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)
‖
2
2
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I
n
th
e
en
d
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th
e
ev
alu
ate
d
r
es
id
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m
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ar
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with
th
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ld
(
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an
d
th
e
f
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lt a
lar
m
is
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elea
s
ed
wh
en
th
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n
d
itio
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is
s
atis
f
i
ed
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; f
au
lt a
lar
m
≤
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; f
au
lt
-
f
r
ee
4.
AP
P
L
I
CA
T
I
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N
T
O
A
T
H
R
E
E
-
T
ANK
SYS
T
E
M
A
th
r
ee
-
tan
k
s
y
s
tem
ap
p
licatio
n
is
u
s
ed
in
th
is
s
tu
d
y
.
T
h
e
s
y
s
tem
is
o
f
ten
u
s
ed
to
ill
u
s
tr
ate
th
e
p
r
in
cip
les
o
f
p
r
o
ce
s
s
co
n
tr
o
l,
s
y
s
tem
d
y
n
am
ics,
a
n
d
f
au
lt
d
e
tectio
n
.
I
n
s
u
ch
a
s
y
s
tem
,
th
e
liq
u
id
lev
els
in
th
e
tan
k
s
an
d
t
h
e
f
lo
w
r
ates
b
et
wee
n
th
em
a
r
e
m
an
a
g
ed
u
s
in
g
s
en
s
o
r
s
,
ac
tu
ato
r
s
,
an
d
co
n
t
r
o
ller
s
.
Au
to
m
atio
n
p
lay
s
a
cr
itical
r
o
le
in
th
is
s
etu
p
b
y
en
s
u
r
i
n
g
th
e
p
r
ec
is
e
r
eg
u
latio
n
o
f
th
ese
v
ar
iab
les
to
ac
h
iev
e
d
esire
d
o
u
tco
m
es,
s
u
ch
as
m
ai
n
tain
in
g
s
p
ec
if
ic
liq
u
id
le
v
els
o
r
f
lo
w
r
ates.
Usi
n
g
ad
v
an
ce
d
au
to
m
atio
n
tech
n
o
lo
g
ies,
s
u
ch
as
p
r
o
g
r
am
m
ab
le
lo
g
ic
c
o
n
tr
o
ller
s
(
PLCs
)
an
d
d
is
tr
ib
u
ted
co
n
t
r
o
l
s
y
s
tem
s
(
DC
S),
th
e
th
r
ee
-
ta
n
k
s
y
s
tem
ca
n
o
p
er
ate
a
u
to
n
o
m
o
u
s
ly
,
a
d
ju
s
tin
g
v
alv
es
an
d
p
u
m
p
s
b
ased
o
n
r
ea
l
-
tim
e
f
ee
d
b
ac
k
f
r
o
m
lev
el
an
d
f
lo
w
s
en
s
o
r
s
.
T
h
is
lev
el
o
f
au
to
m
atio
n
im
p
r
o
v
es
ac
cu
r
ac
y
,
r
ed
u
ce
s
m
an
u
al
in
ter
v
en
tio
n
,
an
d
en
s
u
r
es
co
n
s
is
ten
t
o
p
er
atio
n
ev
e
n
in
co
m
p
lex
s
ce
n
ar
io
s
.
Mo
r
eo
v
er
,
in
teg
r
at
in
g
f
au
lt
d
etec
tio
n
alg
o
r
ith
m
s
in
to
th
e
s
y
s
te
m
en
h
an
ce
s
r
eliab
ilit
y
b
y
i
d
en
tify
in
g
an
o
m
alies
lik
e
s
en
s
o
r
m
alf
u
n
ctio
n
s
,
leak
s
,
o
r
b
l
o
ck
ag
es,
en
a
b
lin
g
p
r
o
ac
tiv
e
m
ai
n
ten
an
ce
.
T
h
u
s
,
th
e
au
to
m
atio
n
o
f
a
th
r
ee
-
t
an
k
s
y
s
tem
s
er
v
es
as
a
f
o
u
n
d
atio
n
al
m
o
d
el
f
o
r
u
n
d
er
s
tan
d
i
n
g
an
d
im
p
lem
e
n
tin
g
co
n
tr
o
l
s
tr
ateg
ies
in
lar
g
er
in
d
u
s
tr
ial
p
r
o
ce
s
s
es
s
u
ch
as
ch
em
ical
m
an
u
f
ac
tu
r
in
g
,
wate
r
t
r
ea
tm
e
n
t,
an
d
o
il r
ef
in
in
g
.
T
h
is
s
ec
tio
n
p
r
esen
ts
s
im
u
la
tio
n
r
esu
lts
th
at
d
em
o
n
s
tr
ate
th
e
ef
f
ec
ti
v
en
ess
o
f
t
h
e
p
r
o
p
o
s
ed
FD
m
eth
o
d
.
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r
s
im
u
latio
n
p
u
r
p
o
s
es,
ab
r
u
p
t
a
n
d
i
n
ter
m
itten
t
f
a
u
lts
ar
e
in
tr
o
d
u
ce
d
in
t
h
e
s
en
s
o
r
s
an
d
ac
tu
ato
r
s
o
f
th
e
ad
v
an
ce
d
t
h
r
ee
-
tan
k
s
y
s
tem
illu
s
tr
ated
in
Fig
u
r
e
1
.
Su
ch
f
au
lts
s
ig
n
if
ican
tly
d
eg
r
a
d
e
s
y
s
tem
p
er
f
o
r
m
an
ce
an
d
ar
e
in
cl
u
d
ed
i
n
th
e
s
tu
d
y
to
ev
alu
ate
th
e
ca
p
ab
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
i
n
id
en
ti
f
y
in
g
th
ese
cr
itical
is
s
u
es.
Mo
d
elin
g
er
r
o
r
s
f
r
o
m
th
e
s
y
s
tem
lin
ea
r
izatio
n
p
r
o
ce
s
s
ar
e
in
co
r
p
o
r
ated
as
n
o
r
m
-
b
o
u
n
d
ed
m
o
d
el
u
n
ce
r
tain
ties
.
T
h
e
b
eh
a
v
io
r
o
f
th
e
th
r
ee
-
tan
k
s
y
s
tem
is
d
escr
ib
ed
b
y
th
e
f
o
llo
win
g
s
et
o
f
n
o
n
lin
ea
r
e
q
u
atio
n
s
,
wh
ich
ca
p
tu
r
e
its
d
y
n
am
ics.
ℎ
̇
1
=
1
−
13
ℎ
̇
2
=
2
+
32
−
20
ℎ
̇
1
=
13
−
32
(
4
1
)
with
13
=
1
13
(
ℎ
1
−
ℎ
3
)
√
2
|
ℎ
1
−
ℎ
3
|
32
=
3
23
(
ℎ
3
−
ℎ
2
)
√
2
|
ℎ
3
−
ℎ
2
|
20
=
2
0
√
2
ℎ
2
Fig
u
r
e
1
.
A
th
r
ee
-
tan
k
s
y
s
tem
[
3
3
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
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b
&
A
u
to
m
,
Vo
l
.
14
,
No
.
2
,
J
u
n
e
20
2
5
:
214
-
2
2
6
222
T
h
e
p
r
o
ce
s
s
o
u
tp
u
ts
y
(
k
)
,
r
e
p
r
esen
ted
b
y
ℎ
3
,
ℎ
2
,
ℎ
1
,
co
r
r
esp
o
n
d
in
g
to
th
e
wate
r
lev
els
in
th
e
r
esp
ec
tiv
e
tan
k
s
.
T
h
e
p
r
o
ce
s
s
in
p
u
ts
u
(
k
)
a
r
e
d
en
o
ted
b
y
Q
1
an
d
Q
2
,
wh
ile
Q
ij
r
ep
r
esen
ts
th
e
f
lo
w
r
ate
o
f
wate
r
f
r
o
m
tan
k
i
-
th
to
ta
n
k
j
-
th
.
Ad
d
itio
n
ally
,
s
13
a
n
d
s
23
r
ef
er
to
th
e
cr
o
s
s
-
s
ec
tio
n
al
ar
ea
s
o
f
th
e
p
ip
es
c
o
n
n
ec
tin
g
th
e
r
esp
ec
tiv
e
tan
k
s
.
T
h
e
c
r
o
s
s
-
s
ec
tio
n
al
ar
ea
o
f
th
e
p
ip
e
co
n
n
ec
ted
t
o
T
a
n
k
2
is
0
.
s
gn
d
en
o
te
s
th
e
s
ign
um
f
u
n
ctio
n
,
wh
ich
is
d
ef
in
e
d
as
s
gn
(
)
=
{
−
1
0
1
<
0
=
0
>
0
13
=
23
=
0
=
T
h
e
s
y
s
tem
'
s
p
r
im
ar
y
p
ar
am
et
er
s
an
d
co
ef
f
icien
ts
ar
e
s
h
o
wn
in
T
ab
le
1
.
I
n
th
e
th
r
ee
-
tan
k
s
y
s
tem
,
an
u
n
k
n
o
wn
d
is
tu
r
b
an
ce
ar
is
es
f
r
o
m
wate
r
f
allin
g
in
to
th
e
ta
n
k
s
f
r
o
m
th
e
p
u
m
p
s
.
Ad
d
itio
n
all
y
,
th
e
s
en
s
o
r
s
u
s
ed
to
m
ea
s
u
r
e
wate
r
le
v
els
in
tr
o
d
u
ce
n
o
is
e
m
ea
s
u
r
em
e
n
t.
Fo
r
f
au
lt
d
etec
tio
n
(
FD)
,
a
lin
ea
r
m
o
d
el
o
f
th
e
s
y
s
tem
is
d
er
iv
ed
b
y
ap
p
ly
in
g
T
ay
l
o
r
s
er
ies
ex
p
an
s
io
n
an
d
lin
e
ar
izin
g
th
e
d
y
n
a
m
ics
ar
o
u
n
d
th
e
eq
u
ilib
r
iu
m
o
r
o
p
er
atin
g
p
o
in
t.
T
h
is
p
r
o
ce
s
s
r
esu
lts
in
a
l
in
ea
r
n
o
m
in
al
m
o
d
el
o
f
th
e
d
is
cr
ete
-
tim
e
s
y
s
tem
in
s
tate
-
s
p
ac
e
f
o
r
m
,
as
s
h
o
wn
in
(
1
)
.
T
h
e
lin
ea
r
izatio
n
is
p
er
f
o
r
m
e
d
at
t
h
e
o
p
er
atin
g
p
o
in
ts
ℎ
1
=
45c
m
,
ℎ
2
=
15c
m
an
d
ℎ
3
=
30c
m
.
No
m
in
al
m
atr
ices a
r
e
o
b
tain
ed
af
ter
lin
ea
r
izin
g
th
e
n
o
n
lin
e
ar
m
o
d
el
o
f
th
e
s
y
s
tem
.
=
[
0
.
9915
0
0
.
0084
0
0
.
9807
0
.
0082
0
.
0084
0
.
0082
0
.
9833
]
;
=
[
0
.
0065
0
.
0008
0
.
0008
0
.
0065
0
0
]
;
=
[
0
.
25
0
0
0
0
.
25
0
0
0
0
.
25
]
;
=
dia
g
[
1
,
1
,
1
]
;
=
0
;
=
;
=
=
dia
g
[
1
,
1
,
1
]
T
h
e
lin
ea
r
izatio
n
p
r
o
c
ess
in
co
r
p
o
r
ates
m
o
d
ellin
g
e
r
r
o
r
s
k
n
o
wn
as
n
o
r
m
-
b
o
u
n
d
e
d
m
o
d
el
u
n
ce
r
tain
ty
in
to
th
e
s
y
s
tem
m
atr
ices,
wh
ich
ar
e
d
e
n
o
ted
as:
1
=
2
=
[
−
0
.
01
0
0
0
−
0
.
01
0
0
0
−
0
.
01
]
;
1
=
[
0
.
01
0
0
.
015
0
0
.
01
0
.
015
0
.
01
0
.
01
0
.
05
]
;
2
=
[
0
.
01
0
0
0
0
.
02
0
0
0
0
]
T
ab
le
1
.
T
h
r
ee
-
tan
k
s
y
s
tem
'
s
p
ar
am
eter
s
[
3
3
]
P
a
r
a
me
t
e
r
s
V
a
l
u
e
U
n
i
t
1
5
4
cm
2
0
.
5
cm
2
62
cm
1
1
0
0
cm
3
/
s
e
c
2
1
0
0
cm
3
/
s
e
c
1
0
.
4
6
2
0
.
6
0
3
0
.
4
5
T
h
e
u
n
ce
r
tain
p
ar
am
eter
(
∑
=
dia
g
[
0
.
9597
,
0
.
9597
,
0
.
9597
]
)
is
ch
o
s
en
at
r
an
d
o
m
an
d
u
n
k
n
o
wn
d
is
tu
r
b
an
ce
,
(
)
∈
[
−
0
.
01
,
0
.
01
]
is
u
s
ed
f
o
r
s
im
u
l
atio
n
s
.
T
h
e
p
u
m
p
in
f
lo
ws
ar
e
ass
u
m
ed
to
b
e
co
n
s
tan
t
with
s
p
ec
if
ied
v
alu
es
o
f
1
=
25
.
6
cm
3
/s
ec
an
d
2
=
39
.
5
cm
3
/s
ec
.
Af
ter
s
o
lv
in
g
th
e
lin
ea
r
m
atr
ix
i
n
eq
u
alities
in
(
1
3
)
an
d
(
1
4
)
,
a
d
is
tu
r
b
an
ce
atten
u
atio
n
lev
el
o
f
γ
=
1
.
0
2
6
an
d
a
f
au
lt
s
en
s
itiv
ity
lev
el
o
f
β
=
1
.
9
8
9
1
ar
e
ac
h
iev
ed
.
T
h
e
co
r
r
esp
o
n
d
in
g
f
ilter
g
ain
m
atr
ix
is
co
m
p
u
ted
u
s
in
g
(
3
9
)
an
d
is
g
iv
en
as
=
[
0
.
3265
−
0
.
0001
−
0
.
0017
∗
6
.
7344
−
0
.
0017
∗
∗
6
.
7265
]
Fu
r
th
er
m
o
r
e
,
th
e
r
esid
u
al
ev
alu
atio
n
f
u
n
ctio
n
is
co
m
p
u
te
d
u
s
in
g
2
n
o
r
m
o
f
th
e
r
esid
u
al
(
4
0
)
an
d
th
e
th
r
esh
o
ld
is
co
m
p
u
ted
as
ℎ
|
=
0
=
‖
(
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‖
2
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(
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∈
2
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up
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0
.
03
.
T
h
e
r
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u
al
in
t
h
e
s
en
s
o
r
/actu
at
o
r
f
au
lt
-
f
r
ee
ca
s
e
is
s
h
o
wn
in
Fig
u
r
e
2.
Fig
u
r
e
3
d
is
p
lay
s
th
e
im
p
ac
t o
f
an
ab
r
u
p
t sen
s
o
r
f
au
lt in
T
an
k
1
o
n
th
e
r
esid
u
al.
A
f
a
u
lt with
a
1
0
cm
o
f
f
s
et
is
in
tr
o
d
u
ce
d
to
th
e
s
en
s
o
r
in
p
u
t
o
f
T
an
k
1
at
t
=
8
0
s
ec
.
T
h
e
s
im
u
latio
n
r
esu
lts
co
n
f
ir
m
th
at
th
e
f
au
lt
is
s
u
cc
ess
f
u
lly
d
etec
ted
.
C
o
m
p
a
r
ab
le
r
esp
o
n
s
es
an
d
s
u
cc
ess
f
u
l
d
etec
tio
n
s
ar
e
also
o
b
s
er
v
ed
f
o
r
f
au
lts
in
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
Desig
n
o
f H
-
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a
s
ed
fa
u
lt
d
etec
tio
n
filt
er fo
r
lin
ea
r
u
n
ce
r
ta
in
s
ystem
s
…
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Ma
s
o
o
d
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h
m
a
d
)
223
o
th
er
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en
s
o
r
s
.
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s
h
o
wn
in
Fig
u
r
e
3
,
th
e
e
v
alu
atio
n
f
u
n
cti
o
n
r
em
ain
s
b
el
o
w
th
e
th
r
esh
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ld
p
r
i
o
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f
a
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cc
u
r
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ce
b
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t
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th
e
th
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en
th
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en
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o
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lt
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cc
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r
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at
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ly
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Fig
u
r
e
4
d
em
o
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s
tr
ates
th
e
r
esp
o
n
s
e
w
h
en
an
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ter
m
itten
t
f
a
u
lt
is
ap
p
lied
to
th
e
ac
tu
ato
r
o
f
P
u
m
p
1
.
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h
e
r
esu
lts
h
ig
h
lig
h
t
t
h
at
th
e
f
a
u
lt
d
etec
t
io
n
f
ilter
ef
f
ec
tiv
ely
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e
n
tifie
d
f
au
lts
in
th
e
d
is
cr
ete
-
tim
e
s
y
s
tem
,
ev
en
i
n
th
e
p
r
esen
ce
o
f
u
n
k
n
o
wn
d
is
tu
r
b
a
n
ce
s
an
d
m
o
d
el
u
n
ce
r
tain
ty
.
Fig
u
r
e
2
.
R
esid
u
al
in
a
f
au
lt
-
f
r
ee
ca
s
e
Fig
u
r
e
3
.
An
ab
r
u
p
t sen
s
o
r
FD in
T
an
k
1
R
em
ar
k
:
I
n
s
ec
tio
n
3
,
two
lin
ea
r
m
atr
ix
in
e
q
u
alities
(
L
MI
s
)
ar
e
d
er
iv
e
d
f
o
r
f
au
lt
d
ete
ctio
n
(
FD)
in
lin
ea
r
u
n
ce
r
tain
s
y
s
tem
s
.
An
H
-
in
d
ex
-
b
ased
f
au
lt
-
s
en
s
itiv
e
f
ilter
is
d
esig
n
ed
to
im
p
r
o
v
e
th
e
f
a
u
lt
s
en
s
itiv
ity
o
f
th
e
r
esid
u
al.
Ho
wev
er
,
th
is
f
ilter
a
ls
o
ex
h
ib
its
s
en
s
itiv
ity
to
d
is
tu
r
b
an
ce
s
an
d
m
o
d
el
u
n
ce
r
tain
ti
es.
I
n
c
o
n
tr
ast,
th
e
H∞
FD
f
ilter
en
s
u
r
es
d
is
tu
r
b
an
ce
atten
u
atio
n
b
u
t
also
p
r
o
v
id
es
r
o
b
u
s
tn
ess
ag
ain
s
t
f
au
lts
.
T
o
ad
d
r
ess
th
ese
ch
allen
g
es,
a
m
u
lti
-
o
b
jectiv
e
H
-
/H∞
b
ased
FD
f
i
lter
is
p
r
o
p
o
s
ed
,
wh
ich
s
im
u
ltan
eo
u
s
ly
o
f
f
er
s
r
o
b
u
s
tn
ess
to
d
is
tu
r
b
an
ce
s
an
d
m
o
d
el
u
n
c
er
tain
ties
,
as
well
as
s
en
s
itiv
ity
to
f
au
lts
.
R
ath
er
th
a
n
m
ax
im
izin
g
β
an
d
m
in
im
izin
g
γ
s
ep
ar
ately
,
th
e
p
er
f
o
r
m
a
n
ce
in
d
ex
,
β
/
γ
,
is
m
ax
im
ized
in
th
is
d
esig
n
.
I
t
is
im
p
o
r
tan
t
to
n
o
te
th
at
th
e
r
esid
u
al
g
en
e
r
ated
b
y
th
e
H
-
/H∞
b
ased
f
ilter
m
ay
b
e
le
s
s
s
en
s
i
tiv
e
th
an
th
at
p
r
o
d
u
ce
d
b
y
th
e
H
-
in
d
e
x
-
b
ased
f
au
lt
-
s
en
s
itiv
e
f
ilter
.
S
im
ilar
ly
,
th
e
r
esid
u
al
f
r
o
m
t
h
e
H
-
/H∞
b
ased
f
ilter
m
ig
h
t
b
e
less
r
o
b
u
s
t
to
d
is
tu
r
b
an
ce
s
an
d
m
o
d
el
u
n
ce
r
tain
ties
co
m
p
ar
ed
to
th
e
r
esid
u
al
f
r
o
m
th
e
H∞
b
ased
f
ilter
.
Nev
er
th
eless
,
th
e
p
r
o
p
o
s
ed
H
-
/H∞
b
ased
FD
f
ilter
is
ad
v
a
n
tag
eo
u
s
as
it
ac
h
iev
es
b
o
t
h
d
is
tu
r
b
an
ce
atten
u
atio
n
a
n
d
f
au
lt
s
en
s
itiv
ity
s
im
u
ltan
eo
u
s
ly
.
Evaluation Warning : The document was created with Spire.PDF for Python.