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h
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ro
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ix
e
d
∞
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ro
b
u
st
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p
ti
m
iza
ti
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n
p
ro
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lem
to
m
a
k
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th
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s
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m
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istu
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e
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o
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a
n
d
a
n
d
f
a
u
lt
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se
n
siti
v
e
o
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th
e
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th
e
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h
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n
d
.
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h
e
n
,
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f
f
icie
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t
c
o
n
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it
io
n
s
w
e
r
e
o
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tai
n
e
d
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lv
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th
e
p
r
o
b
lem
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th
e
li
n
e
a
r
m
a
tri
x
in
e
q
u
a
li
ty
(
LM
I
)
m
o
d
e
.
F
in
a
ll
y
,
th
e
e
ff
e
c
ti
v
e
n
e
ss
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n
d
su
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rit
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o
f
th
e
m
e
th
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w
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r
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d
e
m
o
n
stra
ted
b
y
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m
u
latin
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e
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ti
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s
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n
a
sin
g
le
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in
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tes
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ey
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s
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lt d
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ctio
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r
m
atr
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i
n
eq
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alit
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Ob
s
er
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T
h
is i
s
a
n
o
p
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n
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c
c
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ss
a
rticle
u
n
d
e
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th
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CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
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r
:
He
y
d
ar
T
o
o
s
s
ian
S
h
a
n
d
iz
Dep
ar
t
m
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
Fer
d
o
w
s
i U
n
i
v
er
s
it
y
o
f
Ma
s
h
h
ad
A
za
d
i Sq
u
ar
e,
Ma
s
h
h
ad
,
I
r
an
E
m
ail:
h
to
o
s
ian
@
f
er
d
o
w
s
i.u
m
.
ac
.
ir
1.
I
NT
RO
D
UCT
I
O
N
Fra
ctio
n
ca
lc
u
latio
n
s
m
ad
e
t
h
eir
w
a
y
t
h
r
o
u
g
h
e
n
g
i
n
ee
r
i
n
g
a
n
d
ap
p
licatio
n
af
ter
3
0
0
y
ea
r
s
a
n
d
m
er
el
y
th
eo
r
etica
l
s
tu
d
ie
s
in
m
at
h
e
m
a
tics
[
1
]
-
[
1
8
]
.
Giv
en
d
if
f
er
en
t
a
n
d
n
e
w
m
at
h
e
m
atics
p
r
o
v
id
ed
in
f
r
ac
tio
n
ca
lcu
latio
n
s
,
d
eb
ates in
v
ar
io
u
s
f
ield
s
s
u
c
h
as c
o
n
tr
o
l th
eo
r
y
r
eq
u
ir
e
n
e
w
p
r
o
o
f
s
an
d
th
eo
r
e
m
s
.
As a
r
esu
lt,
t
h
e
f
u
n
d
a
m
en
ta
l
asp
ec
t
s
o
f
f
r
ac
t
io
n
al
-
o
r
d
er
s
y
s
te
m
s
(
FO
Ss
)
w
er
e
i
n
v
est
ig
ated
,
a
n
d
s
tab
il
it
y
t
h
eo
r
e
m
s
w
er
e
p
r
o
p
o
s
ed
[
1
9
]
-
[
2
2
]
.
Ho
w
e
v
er
,
m
a
n
y
asp
ec
ts
r
e
m
ai
n
o
p
en
,
with
s
o
m
e
o
f
t
h
e
m
b
ein
g
c
u
r
r
en
tl
y
s
tu
d
ied
.
O
n
e
o
f
s
u
c
h
asp
ec
ts
i
s
f
a
u
lt
d
etec
tio
n
(
FD)
in
FOS
s
,
w
h
ic
h
is
o
f
g
r
e
at
i
m
p
o
r
tan
ce
.
A
cc
o
r
d
in
g
to
s
ea
r
ch
es,
th
er
e
h
a
v
e
b
ee
n
f
e
w
s
t
u
d
ies
i
n
t
h
is
ar
e
a.
A
r
ib
i
et
a
l.
[
2
3
]
p
r
esen
t
th
r
ee
m
e
th
o
d
s
to
e
v
alu
a
te
f
r
ac
tio
n
al
r
e
s
id
u
al.
A
r
ib
i
et
a
l.
[
2
4
]
,
d
iag
n
o
s
i
s
m
eth
o
d
s
i
n
FO
t
h
er
m
al
s
y
s
te
m
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
.
T
h
e
FD
co
n
tr
o
l
o
f
FO
Ss
i
s
in
v
e
s
ti
g
ated
in
[
2
5
]
.
Z
h
o
n
g
e
t
a
l
.
[
2
6
]
tr
ied
to
f
in
d
a
w
a
y
to
s
o
lv
e
t
h
e
f
a
u
lt
d
etec
tio
n
o
b
s
er
v
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d
esig
n
p
r
o
b
le
m
f
o
r
f
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ac
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al
-
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te
m
s
.
T
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s
u
b
j
ec
t
is
p
r
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is
el
y
t
h
e
s
a
m
e
a
s
th
e
s
u
b
j
ec
t
o
f
t
h
is
ar
t
icle.
Ho
w
e
v
er
,
th
e
y
w
er
e
u
tter
l
y
u
n
s
u
cc
es
s
f
u
l
b
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ca
u
s
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co
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ld
n
o
t
p
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v
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e
s
tab
ilit
y
o
f
th
e
clo
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ed
-
lo
o
p
s
y
s
te
m
,
an
d
th
e
p
u
b
lis
h
ed
ar
ticle
h
as
v
er
y
u
n
d
en
iab
le
f
la
w
s
.
Var
io
u
s
m
et
h
o
d
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
to
d
etec
t
f
au
lt
s
[
2
7
]
-
[
3
3
]
.
On
e
o
f
t
h
ese
m
eth
o
d
s
is
t
h
e
m
o
d
el
-
b
ased
FD
tech
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iq
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e,
w
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h
a
s
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ee
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ac
tically
e
m
p
lo
y
ed
in
m
a
n
y
i
n
d
u
s
tr
ial
ap
p
licatio
n
s
[
3
4
]
-
[
3
8
]
.
Fig
u
r
e
1
illu
s
tr
ates
th
e
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o
r
ith
m
o
f
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h
e
m
o
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b
a
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FD
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o
d
.
Di
s
tu
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d
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le
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p
ical
f
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ee
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i
n
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
A
n
LM
I
a
p
p
r
o
a
c
h
to
Mixed
H
_
∞
/H_
-
fa
u
lt d
etec
tio
n
o
b
s
erver d
esig
n
fo
r
…
(
Mo
h
a
mma
d
A
z
imi
)
1949
th
e
s
y
s
te
m
.
Fo
r
t
h
i
s
r
ea
s
o
n
,
r
o
b
u
s
t
f
au
lt
d
etec
tio
n
s
y
s
te
m
s
h
av
e
b
ee
n
d
e
s
ig
n
ed
.
I
n
a
f
au
l
t
d
etec
tio
n
s
y
s
te
m
,
r
o
b
u
s
tn
es
s
is
d
e
f
in
ed
as t
h
e
s
y
s
te
m
’
s
s
e
n
s
iti
v
it
y
to
f
a
u
lt
s
an
d
r
esis
tan
ce
a
g
ai
n
s
t
u
n
k
n
o
w
n
i
n
p
u
ts
[
3
9
]
-
[
4
2
]
.
T
h
e
m
ai
n
ch
alle
n
g
e
is
n
o
w
to
im
p
le
m
en
t
th
e
m
o
d
el
-
b
ased
f
au
lt
d
etec
tio
n
al
g
o
r
ith
m
o
n
FOSs
an
d
m
ak
e
t
h
e
s
y
s
te
m
d
is
t
u
r
b
an
ce
-
r
esis
ta
n
t
o
n
th
e
o
n
e
h
an
d
a
n
d
f
au
lt
-
s
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n
s
iti
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o
n
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h
e
o
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er
h
a
n
d
.
A
d
d
itio
n
al
l
y
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it
is
w
ell
-
k
n
o
w
n
t
h
at
t
h
e
u
s
e
o
f
lin
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r
m
a
tr
ix
i
n
eq
u
ali
t
y
(
L
MI
)
ca
n
eli
m
i
n
ate
r
estrictio
n
s
o
n
co
n
v
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n
tio
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al
ap
p
r
o
ac
h
es,
an
d
ca
n
b
e
u
s
ed
t
o
s
o
lv
e
p
r
o
b
le
m
s
i
n
v
o
l
v
i
n
g
m
u
ltip
le
m
atr
i
x
v
ar
iab
les.
B
esid
es
t
h
o
s
e
,
d
if
f
er
e
n
t
s
tr
u
ct
u
r
es
ca
n
b
e
i
m
p
o
s
ed
o
n
th
e
s
e
m
atr
ices
[
4
3
]
-
[
4
6
]
.
T
o
th
i
s
e
n
d
,
th
e
p
r
o
b
lem
w
as
tr
an
s
f
o
r
m
ed
i
n
to
t
h
e
m
i
x
ed
∞
/
−
r
o
b
u
s
t
o
p
ti
m
izatio
n
p
r
o
b
lem
,
also
p
r
esen
t
t
h
e
r
es
u
lts
i
n
li
n
ea
r
m
atr
i
x
i
n
eq
u
ali
ties
(
L
MI
s
)
r
o
b
u
s
t c
o
n
tr
o
l th
eo
r
etica
l f
r
a
m
e
w
o
r
k
.
Fig
u
r
e
1
.
Mo
d
el
-
b
ased
f
au
lt d
i
ag
n
o
s
is
al
g
o
r
ith
m
T
h
e
r
est
o
f
t
h
e
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
s
.
I
n
s
ec
tio
n
2
,
i
m
p
le
m
en
ta
tio
n
o
f
t
h
e
m
o
d
el
-
b
ased
tech
n
iq
u
e
o
n
t
h
e
FOS,
as
w
e
ll
as,
th
e
p
r
eli
m
i
n
ar
ies
a
n
d
th
e
p
r
o
b
lem
s
tate
m
e
n
t
ar
e
g
i
v
en
.
T
h
e
s
o
lu
tio
n
s
to
t
h
e
FD
p
r
o
b
lem
f
o
r
FOSs
ar
e
p
r
esen
ted
in
s
ec
t
io
n
3
.
A
ls
o
,
s
o
m
e
s
i
m
u
latio
n
ex
a
m
p
les
ar
e
g
iv
en
i
n
s
ec
tio
n
5
to
illu
s
tr
ate
t
h
e
r
esu
lts
.
F
in
al
l
y
,
s
o
m
e
co
n
cl
u
d
i
n
g
r
e
m
ar
k
s
ar
e
p
r
o
v
id
ed
in
s
ec
tio
n
6
.
No
tatio
n
s
:
d
en
o
ted
th
e
tr
an
s
p
o
s
e
o
f
a
m
atr
i
x
,
its
co
n
j
u
g
ate
̅
an
d
its
co
n
j
u
g
ate
tr
an
s
p
o
s
e
∗
.
(
)
is
s
h
o
r
t
f
o
r
+
∗
,
an
d
ma
x
(
)
r
ep
r
esen
ts
th
e
m
a
x
i
m
u
m
s
in
g
u
lar
v
al
u
e
o
f
.
2.
SYST
E
M
DE
SCRI
P
T
I
O
N
A
ND
P
RO
B
L
E
M
ST
AT
E
M
E
NT
C
o
n
s
id
er
th
e
f
o
llo
w
i
n
g
FOS:
G
:
{
D
α
x
(
t
)
=
Ax
(
t
)
+
Bu
(
t
)
+
B
d
d
(
t
)
+
B
f
f
(
t
)
y
(
t
)
=
Cx
(
t
)
+
Du
(
t
)
+
D
d
d
(
t
)
+
D
f
f
(
t
)
x
(
t
)
=
x
(
0
)
t
∈
[
-
h
1
,
0
]
(
1
)
S
y
s
te
m
G
is
t
h
e
s
tate
s
p
ac
e
f
o
r
m
o
f
a
ti
m
e
-
i
n
v
ar
ian
t
lin
ea
r
FOS
w
h
er
e
D
is
th
e
d
if
f
er
-
i
n
te
g
r
al
o
p
er
ato
r
an
d
0
<
<
1
.
(
t
)
∈
ℝ
d
en
o
tes
th
e
p
s
eu
d
o
-
s
ta
te
v
e
cto
r
.
(
t
)
∈
ℝ
d
en
o
tes
th
e
m
ea
s
u
r
ed
o
u
tp
u
t.
∈
ℝ
×
,
∈
ℝ
×
,
∈
ℝ
×
,
∈
ℝ
×
,
∈
ℝ
×
an
d
∈
ℝ
×
ar
e
co
n
s
tan
t
m
atr
ice
s
.
T
h
e
(
0
)
,
s
tan
d
f
o
r
in
itial
co
n
d
itio
n
d
e
f
i
n
ed
o
n
[
−
ℎ
1
,
0
]
w
h
er
e
ℎ
1
∈
ℝ
an
d
0
<
ℎ
1
.
T
h
is
FOS
a
f
f
ec
ted
b
y
d
is
tu
r
b
an
ce
(
t
)
∈
ℝ
as
an
u
n
w
an
ted
in
p
u
t
an
d
f
a
u
lt
(
t
)
∈
ℝ
in
p
u
t
a
s
a
b
u
g
i
n
t
h
e
s
y
s
t
e
m
.
I
f
t
h
er
e
is
a
p
r
o
b
le
m
i
n
r
ea
d
in
g
an
d
s
e
n
d
in
g
d
ata,
o
r
i
n
m
ea
s
u
r
e
m
en
t,
it
i
s
r
e
f
er
r
ed
to
as
a
s
e
n
s
o
r
f
au
lt
(
)
,
w
h
ic
h
is
r
ep
r
esen
ted
b
y
co
n
s
id
er
in
g
B
f
=
in
th
e
o
u
t
p
u
t e
q
u
atio
n
o
f
t
h
e
s
y
s
te
m
as (
2
)
[
4
7
]
.
y
(
t
)
=
Cx
(
t
)
+
D
d
d
(
t
)
+
(
)
(
2
)
I
f
th
er
e
i
s
a
p
r
o
b
le
m
w
it
h
ac
t
u
ato
r
s
'
p
er
f
o
r
m
a
n
ce
,
it
a
f
f
ec
ts
th
e
i
n
p
u
t
o
f
t
h
e
s
y
s
te
m
an
d
ca
lls
it
a
n
ac
t
u
ato
r
f
au
lt
:
D
α
x
(
t
)
=
A
x
(
t
)
+
B
(
u
(
t
)
+
(
t
)
)
+
B
d
d
(
t
)
y
(
t
)
=
C
x
(
t
)
+
D
(
u
(
t
)
+
(
t
)
)
+
D
d
d
(
t
)
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
Vo
l.
19
,
No
.
6
,
Dec
em
b
er
2
0
2
1
:
1
9
4
8
-
1961
1950
b
y
ad
d
in
g
th
e
p
r
o
ce
s
s
f
au
l
t
(
t
)
ac
co
r
d
in
g
to
its
lo
ca
tio
n
an
d
t
y
p
e
an
d
co
n
s
id
er
in
g
B
f
=
an
d
D
f
=
,
g
en
er
all
y
,
i
n
th
i
s
m
e
th
o
d
,
ad
d
itiv
e
f
a
u
lt
s
f
o
r
d
escr
ib
in
g
th
e
f
au
l
t
is
co
n
s
id
er
ed
f
o
r
th
e
s
y
s
te
m
w
it
h
s
e
n
s
o
r
,
ac
tu
ato
r
an
d
p
r
o
ce
s
s
f
a
u
lts
.
As
a
r
esu
lt,
th
e
f
a
u
lts
ca
n
b
e
r
e
w
r
itten
as
:
(
)
=
[
(
t
)
(
t
)
(
)
]
,
B
f
=
[
0
]
,
D
f
=
[
]
,
o
n
e
o
f
th
e
b
e
s
t
d
ef
in
it
i
o
n
s
o
f
f
r
a
c
t
i
o
n
a
l
d
e
r
iv
at
iv
es
s
o
f
a
r
in
c
o
n
t
r
o
l
a
p
p
li
c
a
ti
o
n
s
is
th
e
C
a
p
u
t
o
’
s
d
e
f
in
i
ti
o
n
[
4
8
]
:
D
t
α
≜
1
Γ
(
k
−
α
)
∫
f
(
k
)
(
τ
)
(
t
−
τ
)
α
+
1
−
k
d
τ
t
a
a
(
4
)
if
th
e
FOS
(
1
)
is
r
elax
ed
at
=
0
,
t
h
e
tr
an
s
f
er
f
u
n
ctio
n
s
o
f
th
e
s
y
s
te
m
,
in
w
h
ic
h
th
e
f
a
u
lt
an
d
d
is
tu
r
b
an
ce
ar
e
as in
p
u
ts
a
n
d
th
e
o
u
tp
u
t o
f
t
h
e
s
y
s
te
m
co
n
s
id
er
ed
as o
u
tp
u
t a
r
e
as
(
5
)
an
d
(
6
)
,
r
esp
ec
tiv
ely
[
4
9
]
:
(
)
=
(
−
)
−
1
+
(
5
)
(
)
=
(
−
)
−
1
+
(
6
)
ac
co
r
d
in
g
to
Fi
g
u
r
e
1
,
a
f
ter
d
eter
m
in
i
n
g
t
h
e
d
y
n
a
m
ic
al
e
q
u
atio
n
s
o
f
t
h
e
s
y
s
te
m
w
it
h
th
e
f
au
l
t,
th
e
n
e
x
t
i
m
p
o
r
tan
t
s
tep
is
to
d
ef
i
n
e
a
s
tab
le
o
b
s
er
v
er
f
o
r
th
e
s
y
s
te
m
(
1
)
.
Fo
r
th
is
p
u
r
p
o
s
e,
th
e
o
b
s
er
v
er
F
h
as
b
ee
n
d
esig
n
ed
as
(
7
)
.
:
{
̂
(
)
=
̂
(
)
+
(
)
̂
(
)
=
̂
(
)
(
)
=
(
)
−
̂
(
)
̂
(
)
=
(
)
∈
[
−
ℎ
2
,
0
]
(
7
)
W
h
er
e
̂
(
)
∈
ℝ
d
en
o
tes
th
e
d
etec
tio
n
o
b
s
er
v
er
s
tate
v
ec
to
r
,
̂
(
)
∈
ℝ
r
e
p
r
e
s
en
t
s
th
e
o
u
tp
u
t
esti
m
at
io
n
v
ec
to
r
s
,
(
)
∈
ℝ
is
r
esid
u
al,
a
n
d
∈
ℝ
×
is
th
e
o
b
s
er
v
er
g
ain
.
B
y
t
h
e
co
m
b
in
atio
n
o
f
th
e
f
ilter
(
7
)
,
th
e
s
y
s
te
m
(
1
)
an
d
co
n
s
id
er
in
g
(
)
=
(
)
−
̂
(
)
th
e
f
o
llo
w
in
g
a
u
g
m
e
n
ted
FOS i
s
o
b
tain
ed
:
{
(
)
=
(
−
)
(
)
+
(
−
)
(
)
+
(
−
)
(
)
(
)
=
(
)
+
(
)
+
(
)
(
8
)
T
o
h
av
e
a
r
o
b
u
s
t
FD
s
y
s
te
m
,
th
e
d
esig
n
s
h
o
u
ld
b
e
ca
r
r
ie
d
o
u
t
in
s
u
ch
a
w
a
y
t
h
at
t
h
e
f
o
llo
w
in
g
co
n
d
itio
n
s
ar
e
estab
li
s
h
ed
:
T
h
e
o
b
s
er
v
er
(
7
)
m
u
s
t
b
e
d
esig
n
ed
s
u
c
h
t
h
at
as
y
m
p
to
tical
l
y
s
tab
ilit
y
o
f
t
h
e
au
g
m
en
ted
s
y
s
te
m
(
8
)
is
g
u
ar
a
n
teed
.
T
o
ac
h
iev
e
th
i
s
co
n
d
itio
n
,
|
(
(
(
−
)
)
)
|
>
2
,
w
h
er
e
s
p
ec
(
(
−
)
)
is
th
e
s
et
o
f
eig
e
n
v
al
u
es
o
f
(
−
)
o
r
th
er
e
ex
is
t
>
0
an
d
>
0
s
u
c
h
th
at
(
+
̅
)
<
0
w
h
er
e
=
(
1
−
)
2
is
as
y
m
p
to
ticall
y
s
tab
le
[
5
0
]
.
Fig
u
r
e
2
s
h
o
w
s
t
h
e
s
tab
il
it
y
r
e
g
io
n
f
o
r
th
is
s
y
s
te
m
.
R
o
b
u
s
t
n
es
s
to
d
is
tu
r
b
an
ce
i
n
p
u
t
is
o
n
e
o
f
th
e
m
ai
n
d
esig
n
p
o
in
ts
o
f
t
h
e
FD.
B
y
u
s
i
n
g
∞
o
p
ti
m
izat
io
n
cr
iter
ia,
th
is
p
er
f
o
r
m
a
n
ce
i
n
d
ex
ex
p
r
ess
ed
as
(
9
)
[
5
1
]
.
‖
(
)
‖
2
‖
(
)
‖
2
<
,
>
0
(
9
)
R
o
b
u
s
t
co
n
tr
o
l
b
y
−
o
p
ti
m
izat
io
n
s
cr
iter
ia
is
th
e
b
est
id
ea
f
o
r
s
o
lv
i
n
g
s
y
s
te
m
s
e
n
s
iti
v
it
y
to
f
au
lts
.
P
er
f
o
r
m
a
n
ce
in
d
e
x
(
1
0
)
g
u
ar
an
tees t
h
e
r
esid
u
a
l
'
s
s
e
n
s
i
tiv
it
y
to
f
au
lt
s
,
w
h
ic
h
i
s
ex
p
r
ess
ed
a
s
(
1
0
)
[
5
2
]
.
‖
(
)
‖
2
‖
(
)
‖
2
>
,
>
0
(
1
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
A
n
LM
I
a
p
p
r
o
a
c
h
to
Mixed
H
_
∞
/H_
-
fa
u
lt d
etec
tio
n
o
b
s
erver d
esig
n
fo
r
…
(
Mo
h
a
mma
d
A
z
imi
)
1951
Fig
u
r
e
2
.
Stab
le
r
eg
io
n
ill
u
s
tr
a
tio
n
B
ased
o
n
th
e
th
r
ee
ab
o
v
e
as
s
u
m
p
tio
n
s
,
m
i
x
i
n
g
∞
/
−
is
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
in
th
i
s
w
o
r
k
f
o
r
FDI
d
esig
n
.
T
h
e
f
o
llo
w
in
g
d
ef
in
i
ti
o
n
s
an
d
le
m
m
as
ar
e
u
s
ed
f
o
r
im
p
le
m
e
n
ti
n
g
t
h
e
p
r
o
p
o
s
ed
m
e
th
o
d
.
Def
i
n
itio
n
1
.
[
5
3
]
T
h
e
∞
n
o
r
m
o
f
(
)
f
o
r
FOS (
1
)
is
d
ef
in
ed
as
(
1
1
)
.
‖
‖
_
(
_
∞
)
≜
(
)
≥
0
(
(
)
)
(
1
1
)
L
e
m
m
a
1
:
(
H
-
B
R
)
:
[
5
4
]
C
o
n
s
i
d
er
th
e
FOS (
1
)
an
d
(
)
=
(
−
)
−
1
+
th
en
‖
(
)
‖
∞
<
if
o
n
l
y
i
f
th
er
e
e
x
is
t
>
0
an
d
>
0
s
u
c
h
th
at:
[
(
)
∗
∗
−
∗
−
]
<
0
(
1
2
)
w
h
er
e
=
{
+
−
,
0
<
<
1
1
≤
<
1
=
2
(
1
−
)
L
em
m
a
2
:
[
5
5
]
L
e
t
m
at
r
i
c
es
∈
ℝ
×
,
∈
ℝ
×
,
Φ
∈
2
Θ
∈
(
+
)
a
n
d
∈
2
.
S
e
t
Λ
i
s
d
ef
in
e
d
as
(
1
3
)
.
Λ
(
Φ
,
Ψ
)
≜
{
∈
|
[
]
∗
Φ
[
]
=
0
,
[
]
∗
Ψ
[
]
≥
0
}
(
1
3
)
Fo
r
(
)
≜
(
−
)
−
1
,
th
er
e
h
o
ld
s
:
[
(
)
]
∗
Θ
[
(
)
]
<
0
,
∀
∈
Λ
(
1
4
)
th
er
e
ex
i
s
t
,
∈
an
d
>
0
s
u
ch
t
h
at
:
[
0
]
∗
(
Φ
⊗
+
Ψ
⊗
)
[
0
]
+
Θ
<
0
(
1
5
)
th
en
"
(
15
)
⟹
(
14
)
"
.
Fu
r
t
h
er
m
o
r
e,
if
Λ
r
ep
r
ese
n
ts
a
c
u
r
v
e
i
n
th
e
co
m
p
le
x
p
la
n
e,
th
e
n
h
o
ld
s
"
(
15
)
⟺
(
14
)
"
.
L
e
m
m
a
3
:
[
5
5
]
T
h
e
s
et
Λ
(
Φ
,
Ψ
)
is
d
ef
i
n
ed
as:
Λ
(
Φ
,
Ψ
)
≜
{
∈
|
[
]
∗
Φ
[
]
≥
0
,
[
]
∗
Ψ
[
]
≥
0
}
(
1
6
)
i
f
m
atr
ices
>
0
an
d
>
0
ex
is
t s
u
ch
t
h
at
L
MI
co
n
d
itio
n
(
1
5
)
h
o
ld
s
,
th
en
co
n
d
it
io
n
(
1
4
)
h
o
ld
s
∀
∈
Λ
.
L
e
m
m
a
4
:
(
P
r
o
j
ec
tio
n
lem
m
a)
[
5
6
]
.
Un
s
tr
u
ctu
r
ed
m
atr
i
x
s
atis
f
ies
th
e
f
o
llo
w
i
n
g
eq
u
atio
n
s
if
a
s
y
m
m
etr
i
c
m
atr
i
x
∈
an
d
co
lu
m
n
d
i
m
e
n
s
io
n
,
an
d
m
a
tr
ices e
x
is
t:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
Vo
l.
19
,
No
.
6
,
Dec
em
b
er
2
0
2
1
:
1
9
4
8
-
1961
1952
+
+
<
0
(
1
7
)
if
an
d
o
n
l
y
i
f
:
<
0
(
1
8
)
an
d
<
0
(
1
9
)
co
n
ce
r
n
i
n
g
to
ar
e
s
atis
f
ied
.
W
h
er
e
an
d
ar
e
ar
b
itra
r
y
m
a
tr
ices,
w
h
o
s
e
co
l
u
m
n
s
f
o
r
m
a
b
asis
o
f
th
e
n
u
l
l sp
ac
es o
f
an
d
,
r
esp
ec
tiv
e
l
y
.
L
e
m
m
a
5
:
[
5
7
]
.
T
h
e
FOS
G
(
s
)
is
s
t
ab
le
if
an
d
o
n
l
y
if
‖
(
)
‖
∞
is
b
o
u
n
d
ed
.
3.
M
AIN RES
UL
T
S
I
n
th
i
s
s
ec
tio
n
,
co
n
d
itio
n
s
ii
an
d
iii
ar
e
tr
an
s
f
o
r
m
ed
in
to
L
MI
s
.
C
o
r
o
llar
y
1
u
n
if
ies
t
h
e
th
eo
r
e
m
s
.
T
h
eo
r
em
1
.
T
h
e
s
y
s
te
m
(
8
)
is
s
tab
le,
a
n
d
th
e
p
er
f
o
r
m
an
ce
in
d
ices
(
9
)
is
g
u
ar
an
teed
,
i
f
th
er
e
ex
is
t
p
o
s
iti
v
e
s
ca
lar
p
o
s
itiv
e
d
ef
i
n
ite
s
y
m
m
etr
ic
m
atr
ices
1
,
1
an
d
m
atr
ices
,
s
u
ch
t
h
at
t
h
e
f
o
llo
w
i
n
g
L
MI
s
h
o
ld
:
[
(
Π
)
+
Ξ
2
Ω
+
C
∗
−
(
+
)
Ω
∗
∗
−
2
]
<
0
(
2
0
)
w
h
er
e
Π
=
−
,
Ω
=
−
,
>
0
,
Ξ
2
=
Π
−
+
1
+
1
,
=
,
=
(
1
−
)
2
.
h
o
ld
s
an
d
th
e
f
ilter
g
ai
n
is
o
b
tain
ed
:
=
−
(
2
1
)
P
r
o
o
f
:
B
ased
o
n
d
ef
in
itio
n
1
:
‖
(
)
‖
∞
≜
(
)
≥
0
(
(
)
)
=
(
(
)
≥
0
(
−
̃
)
−
1
̃
+
)
(
2
2
)
w
h
er
e
̃
=
−
̃
=
−
(
2
3
)
b
y
s
o
m
e
b
asic
m
atr
i
x
ca
lcu
lat
i
o
n
s
:
‖
(
)
‖
∞
<
⟺
(
)
(
)
∗
−
2
<
0
∀
(
)
≥
0
⟺
[
(
)
]
∗
Θ
[
(
)
]
<
0
,
∀
∈
Λ
(
24
)
w
h
er
e
(
)
≜
(
−
̃
)
−
1
,
=
,
an
d
Λ
(
Φ
,
Ψ
)
is
d
ef
in
ed
i
n
(
1
3
)
,
also
:
Θ
=
[
−
2
]
(
2
5
)
th
en
ac
co
r
d
in
g
to
L
e
m
m
a
2
,
th
e
last
p
ar
t
o
f
(
2
4
)
is
also
eq
u
iv
ale
n
t
to
th
e
s
tate
m
e
n
t
th
at
∃
1
,
1
∈
,
1
>
0
an
d
1
>
0
s
u
c
h
th
at
t
h
e
L
MI
(
2
4
)
h
o
ld
s
.
[
0
̃
̃
]
(
Φ
⊗
1
+
Ψ
⊗
1
)
[
0
̃
̃
]
+
Θ
<
0
(
2
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
A
n
LM
I
a
p
p
r
o
a
c
h
to
Mixed
H
_
∞
/H_
-
fa
u
lt d
etec
tio
n
o
b
s
erver d
esig
n
fo
r
…
(
Mo
h
a
mma
d
A
z
imi
)
1953
s
i
m
ilar
to
[
5
4
]
,
Φ
=
[
0
̅
0
]
Ψ
=
[
0
̅
0
]
(
2
7
)
n
o
w
th
e
i
n
eq
u
ali
t
y
(
2
6
)
ca
n
b
e
r
ef
o
r
m
u
la
ted
as
<
0
w
h
er
e
an
d
ar
e
g
iv
e
n
b
y
:
=
[
1
+
1
C
1
+
1
0
0
C
0
−
2
]
=
[
0
̃
̃
0
]
(
2
8
)
b
y
d
e
f
in
in
g
t
h
e
m
atr
ice
s
an
d
as
(
2
9
)
.
=
[
0
−
0
0
]
→
=
[
0
]
(
2
9
)
I
t c
an
b
e
o
b
tain
ed
b
y
L
e
m
m
a
4
th
at
in
eq
u
a
lit
y
<
0
is
eq
u
i
v
ale
n
t
to
:
+
[
̃
−
̃
]
[
0
]
+
[
0
]
[
̃
−
̃
]
<
0
(
3
0
)
No
w
b
y
s
u
b
s
t
itu
tin
g
=
in
eq
u
alit
y
(
2
0
)
is
o
b
tain
e
d
,
an
d
th
e
p
r
o
o
f
is
co
m
p
leted
.
T
h
eo
r
em
2
.
T
h
e
au
g
m
e
n
ted
f
r
ac
tio
n
al
-
o
r
d
er
s
y
s
te
m
(
8
)
is
s
tab
le
an
d
it
g
u
ar
a
n
tees
t
h
e
p
er
f
o
r
m
a
n
ce
i
n
d
ex
(
1
0
)
,
if
th
er
e
ex
is
t
p
o
s
i
tiv
e
s
ca
lar
>
0
an
d
s
y
m
m
etr
ic
m
atr
ice
s
2
,
2
an
d
m
a
tr
ices
,
s
u
c
h
th
a
t
th
e
f
o
llo
w
in
g
L
MI
:
[
(
Π
)
−
Ξ
2
Ω
−
C
∗
(
−
)
Ω
∗
∗
−
+
2
]
<
0
(
3
1
)
w
h
er
e
Π
=
−
,
Ω
=
−
,
>
0
,
Ξ
2
=
Π
−
+
2
+
2
,
=
,
=
(
1
−
)
2
.
T
h
e
f
ilter
g
ai
n
is
g
iv
e
n
b
y
(
2
1
)
.
P
r
o
o
f
:
Alth
o
u
g
h
t
h
e
p
r
in
cip
le
s
of
p
r
o
v
in
g
th
is
t
h
eo
r
e
m
ar
e
v
er
y
s
i
m
ilar
to
th
at
T
h
eo
r
e
m
1,
s
in
ce
it
co
n
tai
n
s
s
m
al
l
an
d
ess
e
n
tia
l
p
o
in
ts
,
t
h
e
p
r
o
o
f
of
th
is
t
h
eo
r
e
m
is
f
u
ll
y
a
d
d
r
ess
ed
.
B
ased
o
n
d
ef
in
itio
n
1
:
‖
(
)
‖
∞
≜
(
)
≥
0
(
(
)
)
=
(
(
)
≥
0
C
(
−
̃
)
−
1
̃
+
)
(
3
2
)
w
h
er
e
̃
=
−
,
B
y
a
n
al
y
zin
g
‖
(
)
‖
∞
:
‖
(
)
‖
∞
<
⟺
(
)
(
)
∗
−
2
<
0
∀
(
)
≥
0
⟺
[
(
)
]
∗
Θ
[
(
)
]
<
0
.
∀
∈
Λ
(
3
3
)
w
h
er
e
(
)
≜
(
−
̃
)
−
1
̃
an
d
Λ
(
Φ
,
Ψ
)
is
d
ef
in
ed
in
(
1
1
)
,
also
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
Vo
l.
19
,
No
.
6
,
Dec
em
b
er
2
0
2
1
:
1
9
4
8
-
1961
1954
Θ
=
[
−
−
−
−
2
]
(
3
4
)
th
en
ac
co
r
d
in
g
to
L
e
m
m
a
3
,
th
e
last
p
ar
t o
f
(
2
9
)
is
also
eq
u
iv
alen
t to
th
e
s
tate
m
en
t t
h
at
∃
2
,
2
∈
,
2
>
0
an
d
1
>
0
s
u
c
h
th
at
t
h
e
L
MI
(
2
9
)
h
o
ld
s
.
[
0
̃
B
̃
]
(
Φ
⊗
2
+
Ψ
⊗
2
)
[
0
̃
B
̃
]
+
Θ
<
0
(
3
5
)
s
i
m
ilar
to
[
5
4
]
,
Φ
=
[
0
̅
0
]
Ψ
=
[
0
̅
0
]
(
3
6
)
n
o
w
th
e
i
n
eq
u
ali
t
y
(
2
9
)
ca
n
b
e
r
ef
o
r
m
u
la
ted
as
<
0
w
h
er
e
an
d
ar
e
g
iv
e
n
b
y
:
=
[
−
2
+
2
−
1
+
1
0
0
−
0
−
2
]
=
[
0
̃
B
̃
0
]
(
3
7
)
b
y
d
e
f
in
in
g
t
h
e
m
atr
ice
s
an
d
as
(
3
8
)
.
=
[
0
−
0
0
]
→
=
[
0
]
(
3
8
)
I
t c
an
b
e
o
b
tain
ed
b
y
L
e
m
m
a
4
th
at
in
eq
u
a
lit
y
<
0
is
eq
u
i
v
ale
n
t
to
:
+
[
̃
−
B
̃
]
[
0
]
+
[
0
]
[
̃
−
B
̃
]
<
0
(
3
9
)
No
w
b
y
s
u
b
s
t
itu
tin
g
=
in
eq
u
alit
y
(
3
1
)
is
o
b
tain
e
d
,
an
d
th
e
p
r
o
o
f
is
co
m
p
leted
.
C
o
r
o
llar
y
1
.
So
lv
i
n
g
th
e
f
o
llo
w
i
n
g
co
n
v
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I
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T
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