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0
...
0
0
0
...
...
...
...
...
0
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1
0
0
0
...
0
1
0
1
2
1
n
n
c
c
c
C
k
k
k
K
,...,
,
,
,...,
,
2
1
2
1
T
h
e
s
et
o
f
(
4
)
,
(
5
)
w
il
l tr
an
s
f
o
r
m
in
to
:
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
c
l
a
c
l
a
c
l
a
c
l
a
k
b
k
b
k
b
k
b
x
k
b
a
x
k
b
a
x
k
b
a
x
k
b
a
x
x
x
x
x
x
x
)
(
,...,
)
(
)
(
)
(
...
,...,
)
(
,...,
)
(
)
(
)
(
...
1
3
3
2
2
2
1
1
1
1
3
2
2
1
3
3
2
2
1
1
1
3
3
2
2
2
1
1
1
1
3
2
2
1
(
6
)
No
tice
th
at
in
t
h
e
ab
s
e
n
ce
o
f
t
h
e
ex
ter
n
al
i
m
p
ac
t,
t
h
e
p
r
o
ce
s
s
in
t
h
e
s
et
(
4
)
,
(
5
)
m
u
s
t
a
s
y
m
p
to
ticall
y
ap
p
r
o
ac
h
th
e
p
r
o
ce
s
s
es
o
f
a
s
y
s
te
m
w
i
th
a
co
n
tr
o
ller
,
as
if
t
h
e
clo
s
ed
-
lo
o
p
s
y
s
te
m
ac
co
r
d
i
n
g
to
a
s
tate
v
ec
to
r
,
w
a
s
af
f
ec
ted
b
y
t
h
e
i
m
p
ac
t
o
f
th
e
co
n
v
er
g
e
n
t
d
is
t
u
r
b
an
ce
w
a
v
es
.
T
h
ese
d
is
t
u
r
b
an
ce
s
ar
e
ca
u
s
ed
b
y
t
h
e
)
(
t
K
p
o
ly
n
o
m
in
t
h
e
E
q
u
a
tio
n
(
5
)
.
T
h
e
er
r
o
r
m
u
s
t
co
n
v
er
g
e
a
n
d
th
e
s
p
ee
d
o
f
co
n
v
er
g
e
n
ce
i
s
d
ef
i
n
ed
d
u
r
in
g
t
h
e
s
y
n
t
h
esi
s
o
f
th
e
o
b
s
er
v
er
.
T
h
e
m
ai
n
p
r
o
p
er
ty
o
f
th
e
s
et
(
4
)
an
d
(
5
)
lies
i
n
t
h
e
a
s
y
m
p
to
m
a
tical
s
tab
ili
t
y
.
T
h
i
s
w
a
y
w
e
f
o
u
n
d
th
e
r
eq
u
ir
e
m
e
n
t
f
o
r
th
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as
y
m
p
to
tical
s
tab
ili
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y
o
f
th
e
s
y
s
te
m
u
s
i
n
g
t
h
e
g
r
ad
ien
t
-
v
elo
cit
y
m
et
h
od
o
f
th
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
s
[
8
-
1
1
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
4
,
A
u
g
u
s
t
201
9
:
2
8
7
4
-
2879
2876
Fro
m
(
6
)
w
e
f
in
d
t
h
e
co
m
p
o
n
en
ts
o
f
t
h
e
v
ec
to
r
g
r
ad
i
en
t
f
o
r
th
e
L
y
ap
u
n
o
v
v
ec
to
r
f
u
n
ctio
n
:
))
,
(
)
,
.
.
.
,
,
(
),
,
(
(
)
,
(
2
2
1
x
V
x
V
x
V
x
V
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
c
l
a
x
V
c
l
a
x
V
c
l
a
x
V
x
V
x
V
k
b
x
V
k
b
x
V
k
b
x
V
x
k
b
a
x
x
V
x
k
b
a
x
x
V
x
k
b
a
x
x
V
x
x
x
V
x
x
x
V
x
x
x
V
)
(
)
,
(
,...,
)
(
)
,
(
,
)
(
)
,
(
.
;
..
.,
)
,
(
;
)
,
(
)
,
(
,...,
)
,
(
,
)
,
(
,
)
(
)
,
(
,...,
)
(
)
,
(
,
)
(
)
,
(
;
)
,
(
;.
)
,
(
;.
)
,
(
1
2
2
2
1
2
2
1
1
1
2
3
2
2
2
1
1
2
2
2
1
1
1
1
2
2
1
2
1
1
1
1
3
3
2
2
2
1
(
7
)
Fro
m
(
6
)
w
e
f
i
n
d
th
e
d
ec
o
m
p
o
s
itio
n
o
f
t
h
e
v
elo
cit
y
v
ec
to
r
to
th
e
co
o
r
d
in
ates
).
,...,
,
,...,
(
1
1
n
n
x
x
,
)
(
,...,
)
(
,
)
(
...
;
;
;
,
,...,
,
,
)
(
,...,
)
(
,
)
(
,
,...,
,
1
2
2
1
1
1
1
3
2
2
1
2
2
1
1
1
2
2
1
1
1
3
2
2
1
2
1
3
1
2
1
2
1
3
2
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
x
n
n
n
x
n
n
n
x
n
n
x
n
x
x
c
l
a
dt
d
c
l
a
dt
d
c
l
a
dt
d
dt
d
dt
d
dt
d
k
b
dt
dx
k
b
dt
dx
k
b
dt
dx
x
k
b
a
dt
dx
x
k
b
a
dt
dx
x
k
b
a
dt
dx
x
dt
dx
x
dt
dx
x
dt
dx
n
n
n
n
n
(
8
)
T
o
r
esear
ch
th
e
s
tab
ilit
y
o
f
t
h
e
s
y
s
te
m
(
6
)
w
e
u
s
e
t
h
e
b
asic
s
o
f
L
y
ap
u
n
o
v
’
s
d
ir
ec
t
m
eth
o
d
[
1
4
-
1
6
]
.
Fo
r
th
e
s
y
s
te
m
to
ac
h
ie
v
e
th
e
as
y
m
p
to
tical
eq
u
ilib
r
i
u
m
w
e
n
ee
d
to
s
ec
u
r
e
th
e
ex
is
te
n
ce
o
f
a
p
o
s
itiv
e
f
u
n
ct
io
n
)
,
(
x
V
s
o
th
at
it
s
to
tal
d
er
iv
ati
v
e
o
n
th
e
ti
m
e
ax
is
alo
n
g
t
h
e
s
tate
f
u
n
ctio
n
(
6
)
is
a
n
eg
a
tiv
e
f
u
n
ctio
n
.
T
h
e
to
tal
d
er
iv
ativ
e
f
r
o
m
L
y
ap
u
n
o
v
f
u
n
ctio
n
w
i
th
r
e
g
ar
d
to
th
e
s
tate
E
q
u
atio
n
(
6
)
is
d
ef
i
n
ed
as
a
s
ca
lar
p
r
o
d
u
ct
o
f
th
e
g
r
ad
ie
n
t (
7
)
f
r
o
m
L
y
ap
u
n
o
v
an
d
th
e
v
elo
cit
y
v
ec
to
r
.
(
8
)
:
2
2
1
2
2
2
2
1
2
1
2
2
3
2
2
2
2
2
2
2
2
2
2
2
1
2
1
2
2
2
1
2
3
2
3
2
2
2
2
2
1
2
1
2
1
2
2
3
2
2
2
1
1
1
1
)
(
,...,
)
(
)
(
,...,
)
(
,...,
)
(
)
(
)
(
,...,
)
,
(
)
,
(
)
,
(
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
i
n
k
i
k
i
n
i
n
k
x
i
k
i
c
l
a
c
l
a
c
l
a
k
b
k
b
k
b
x
k
b
a
x
k
b
a
x
k
b
a
x
k
b
a
x
x
x
dt
d
x
V
dt
dx
x
x
V
dt
x
dV
k
k
(
9
)
Fro
m
(
9
)
w
e
d
er
iv
e
th
at
t
h
e
t
o
tal
ti
m
e
d
er
iv
ati
v
e
o
f
t
h
e
v
ec
to
r
f
u
n
c
tio
n
w
il
l
b
e
n
eg
ati
v
e.
L
y
ap
u
n
o
v
f
u
n
ctio
n
f
r
o
m
(
7
)
ca
n
b
e
r
ep
r
esen
ted
in
th
e
s
ca
lar
v
ie
w
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
S
o
lvin
g
o
u
tp
u
t c
o
n
tr
o
l p
r
o
b
le
ms u
s
in
g
Lya
p
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n
o
v
g
r
a
d
ien
t
-
v
elo
city
ve
cto
r
fu
n
ctio
n
(
М.
А
.
B
eisen
b
i)
2877
,
)
1
(
2
1
,...,
)
1
(
2
1
)
1
(
2
1
)
(
2
1
)
1
(
2
1
,...,
)
1
(
2
1
)
1
(
2
1
)
(
2
1
)
(
2
1
,...,
)
(
2
1
)
(
2
1
)
(
2
1
2
1
,...,
2
1
2
1
2
1
,...,
2
1
2
1
2
1
)
(
2
1
,...,
)
(
2
1
)
(
2
1
)
(
2
1
2
1
,...,
2
1
2
1
)
,
(
2
1
2
3
3
3
2
2
2
2
2
1
2
1
1
1
2
1
2
3
3
2
2
2
2
1
2
1
1
2
1
2
3
3
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2
2
1
2
1
1
2
2
3
2
2
2
2
3
3
2
2
2
2
1
1
2
1
2
3
3
2
2
2
2
1
2
1
1
2
2
3
2
2
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
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n
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n
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n
n
n
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n
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n
n
n
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k
b
c
l
a
k
b
c
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k
b
c
l
a
k
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c
l
a
x
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a
x
k
b
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x
k
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с
l
a
c
l
a
c
l
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c
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a
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b
k
b
k
b
k
b
x
k
b
a
x
k
b
a
x
k
b
a
x
k
b
a
x
x
x
x
V
(
1
0
)
T
h
e
co
n
d
itio
n
f
o
r
th
e
p
o
s
iti
v
e
ce
r
tain
t
y
(
1
0
)
i.e
.
ex
is
te
n
ce
o
f
L
y
ap
u
n
o
v
f
u
n
ctio
n
w
ill b
e
d
ef
in
ed
:
0
>
1
...
0
>
1
0
>
1
0
>
1
3
2
2
1
1
n
n
n
n
n
n
n
n
k
b
a
k
b
a
k
b
a
k
b
a
(
1
1
)
0
>
1
...
0
>
1
0
>
1
0
>
1
3
3
2
2
2
1
1
1
n
n
n
n
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n
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n
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n
n
n
n
k
b
c
l
a
k
b
c
l
a
k
b
c
l
a
k
b
c
l
a
(
1
2
)
T
h
e
q
u
alit
y
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d
th
e
s
tab
ilit
y
o
f
th
e
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n
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o
l
s
y
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is
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ictat
ed
b
y
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e
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m
e
n
t
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o
f
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m
a
tr
ix
o
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s
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te
m
.
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eter
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g
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te
m
w
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p
r
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d
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e
s
m
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tr
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s
itio
n
al
p
r
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s
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a
s
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te
m
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d
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g
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q
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co
n
tr
o
l.
T
h
e
s
et
o
f
i
n
eq
u
alit
ies
(
1
1
)
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d
(
1
2
)
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er
v
e
as
t
h
e
n
ec
es
s
ar
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itio
n
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e
r
o
b
u
s
t
d
y
n
a
m
ic
eq
u
alize
r
.
T
h
e
co
n
d
itio
n
(
1
1
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allo
w
s
f
o
r
t
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s
tab
ilit
y
i
n
th
e
s
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te
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ec
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r
.
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ag
in
e
a
co
n
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o
l
s
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m
w
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a
s
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o
f
d
esire
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an
s
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r
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s
s
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h
o
n
e
in
p
u
t
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d
o
n
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o
u
tp
u
t:
n
n
n
n
n
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d
x
d
x
d
x
d
x
x
x
x
x
x
x
1
3
2
2
1
1
1
3
2
2
1
,...,
...
(
1
3
)
E
x
p
lo
r
e
th
e
s
y
s
te
m
(
1
3
)
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ef
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,...,
1
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I
SS
N
:
2
0
8
8
-
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I
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p
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(
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.
3.
CO
NCLU
SI
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in
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o
m
ial
w
it
h
a
m
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d
al
co
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tr
o
l
w
i
th
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
S
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.
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eisen
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i)
2879
th
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d
esire
w
i
th
o
u
t e
x
tr
an
eo
u
s
ca
lc
u
latio
n
s
.
RE
F
E
R
E
NC
E
S
[1
]
A
n
d
riev
sk
y
B
.
R
.
a
n
d
F
ra
tk
o
v
A
.
L
.,
“
S
e
lec
ted
c
h
a
p
ters
o
f
th
e
t
h
e
o
ry
o
f
a
u
to
m
a
ti
c
c
o
n
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w
it
h
e
x
a
m
p
le
s
in
th
e
lan
g
u
a
g
e
M
ATLA
B
–
SPb
,”
Na
u
k
a
,
pp.
4
7
5
,
2
0
0
0
.
[2
]
Kv
a
k
e
rn
a
h
H.
a
n
d
S
iv
a
n
R.
,
“
L
in
e
a
r
o
p
ti
m
a
l
c
o
n
tro
l
sy
ste
m
s
,”
M
.
M
ir,
p
p
.
6
5
0
,
1
9
8
6
.
[3
]
A
n
d
re
e
v
Y
.
N.
,
“
M
a
n
a
g
in
g
f
in
it
e
-
d
im
e
n
sio
n
a
l
li
n
e
a
r
o
b
jec
ts
,”
M
.
N
a
u
k
a
,
p
p
.
4
2
4
,
1
9
7
6
.
[4
]
Re
y
U.
,
“
T
e
c
h
n
iq
u
e
s f
o
r
m
a
n
a
g
in
g
tec
h
n
o
lo
g
ica
l
p
r
o
c
e
ss
e
s
,”
M
.
M
ir,
p
p
.
6
3
8
,
1
9
8
3
.
[5
]
Ku
k
h
a
re
n
k
o
N.
V.
,
“
S
y
n
th
e
sis
o
f
m
o
d
a
l
re
g
u
lato
rs
w
it
h
i
n
c
o
m
p
le
te
c
o
n
tr
o
ll
a
b
il
it
y
o
f
o
b
jec
ts
,”
Iz
v
e
stiy
a
Ak
a
d
e
m
ii
Na
u
k
.
Ru
ss
ian
A
c
a
d
e
m
y
o
f
S
c
ien
c
e
s.
T
e
c
h
n
ica
l
c
y
b
e
rn
e
ti
c
s
,
n
o
.
3
.
[6
]
G
a
n
t
m
a
k
h
e
r
F
.
R
.,
“
T
h
e
o
ry
o
f
m
a
tri
c
e
s
,”
M
o
sc
o
w
,
Na
u
k
a
,
1
9
6
7
.
[7
]
W
.
S
treitz,
“
T
h
e
m
e
th
o
d
o
f
th
e
s
p
a
c
e
o
f
sta
tes
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th
e
th
e
o
ry
o
f
d
isc
re
te
li
n
e
a
r
c
o
n
tro
l
sy
ste
m
s,
P
e
r.
w
it
h
En
g
li
sh
,”
M
o
sc
o
w
,
Na
u
k
a
,
1
9
8
5
.
[8
]
Be
ise
n
b
i
M
.
A.
,
“
In
v
e
stig
a
ti
o
n
o
f
ro
b
u
st
sta
b
i
li
ty
o
f
a
u
to
m
a
ti
c
c
o
n
tro
l
sy
ste
m
s
b
y
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e
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o
d
o
f
f
u
n
c
ti
o
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s
o
f
A
M
Ly
a
p
u
n
o
v
,”
A
sta
n
a
,
p
p
.
2
0
4
,
2
0
1
5
.
[9
]
Be
ise
n
b
i
M
.
a
n
d
Us
k
e
n
b
a
y
e
v
a
G
.
,
“
T
h
e
Ne
w
A
p
p
ro
a
c
h
o
f
De
sig
n
Ro
b
u
st
S
tab
i
li
ty
f
o
r
L
in
e
a
r
Co
n
tr
o
l
S
y
ste
m
,”
Pro
c
.
o
f
th
e
I
n
tl
.
Co
n
f.
o
n
Ad
v
a
n
c
e
s in
El
e
c
tro
n
ics
a
n
d
El
e
c
trica
l
T
e
c
h
n
o
l
o
g
y
—
AE
ET
,
p
p
.
11
-
18
,
2
0
1
4
.
[1
0
]
Be
ise
n
b
i
M
.
a
n
d
Ye
rm
e
k
b
a
y
e
v
a
J.
,
“
Co
n
stru
c
ti
o
n
o
f
Ly
a
p
u
n
o
v
f
u
n
c
ti
o
n
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o
e
x
a
m
in
e
Ro
b
u
st
S
ta
b
il
it
y
f
o
r
L
in
e
a
r
S
y
st
e
m
,”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Co
n
tr
o
l
,
En
e
rg
y
a
n
d
El
e
c
trica
l
E
n
g
i
n
e
e
rin
g
(
CEE
E)
,
vol
.
1
,
p
p
.
17
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