T
E
L
KO
M
N
I
KA
T
e
lec
om
m
u
n
icat
ion
,
Com
p
u
t
i
n
g,
E
lec
t
r
on
ics
an
d
Cont
r
ol
Vol.
18
,
No.
3
,
J
une
2020
,
pp.
1483
~
1490
I
S
S
N:
1693
-
6
930,
a
c
c
r
e
dit
e
d
F
ir
s
t
G
r
a
de
by
Ke
me
nr
is
tekdikti
,
De
c
r
e
e
No:
21/E
/KP
T
/2018
DO
I
:
10.
12928/
T
E
L
KO
M
NI
KA
.
v18i3.
13672
1483
Jou
r
n
al
h
omepage
:
ht
tp:
//
jour
nal.
uad
.
ac
.
id/
index
.
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E
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OM
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A
C
h
aos syn
c
h
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iz
at
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a 6
-
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h
yp
e
r
c
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ao
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ic
syste
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se
lf
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x
c
ite
d
at
t
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a
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t
or
Ahm
e
d
S
.
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-
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e
id
i
,
S
aad
F
awz
i
A
l
-
Az
z
awi
D
ep
ar
t
men
t
o
f
Mat
h
emat
i
cs
,
Co
l
l
e
g
e
o
f
Co
m
p
u
t
er
Sci
e
n
ces
an
d
Ma
t
h
ema
t
i
c
s
,
U
n
i
v
er
s
i
t
y
o
f
M
o
s
u
l
,
Mo
s
u
l
,
Iraq
Ar
t
icle
I
n
f
o
AB
S
T
RA
CT
A
r
ti
c
le
h
is
tor
y
:
R
e
c
e
ived
J
ul
22
,
2019
R
e
vis
e
d
J
a
n
29
,
2020
Ac
c
e
pted
F
e
b
23
,
2020
T
h
i
s
p
ap
er
p
re
s
en
t
ed
s
t
a
b
i
l
i
t
y
ap
p
l
i
cat
i
o
n
fo
r
ch
a
o
s
s
y
n
ch
r
o
n
i
zat
i
o
n
u
s
i
n
g
a
6
-
D
h
y
p
erc
h
a
o
t
i
c
s
y
s
t
em
o
f
d
i
fferen
t
co
n
t
r
o
l
l
ers
a
n
d
t
w
o
t
o
o
l
s
:
L
y
ap
u
n
o
v
s
t
a
b
i
l
i
t
y
t
h
eo
r
y
an
d
L
i
n
eari
z
at
i
o
n
met
h
o
d
s
.
Sy
n
c
h
ro
n
i
z
at
i
o
n
met
h
o
d
s
b
as
e
d
o
n
n
o
n
l
i
n
ear
co
n
t
r
o
l
s
t
rat
e
g
y
i
s
u
s
ed
.
T
h
e
s
e
l
ect
i
n
g
co
n
t
ro
l
l
e
r's
met
h
o
d
s
h
a
v
e
b
een
mo
d
i
fi
e
d
b
y
ap
p
l
y
i
n
g
co
mp
l
et
e
s
y
n
c
h
ro
n
i
za
t
i
o
n.
T
h
e
L
i
n
e
a
r
i
z
a
t
i
o
n
m
e
t
h
o
d
s
c
a
n
a
c
h
i
e
v
e
c
o
n
v
e
r
g
e
n
c
e
a
c
c
o
r
d
i
n
g
t
o
t
h
e
o
f
c
o
m
p
l
e
t
e
s
y
n
c
h
r
o
n
i
z
a
t
i
o
n
.
N
u
mer
i
cal
s
i
m
u
l
a
t
i
o
n
s
are
carri
e
d
o
u
t
b
y
u
s
i
n
g
M
A
T
L
A
B
t
o
v
al
i
d
a
t
e
t
h
e
effect
i
v
en
e
s
s
o
f
t
h
e
an
a
l
y
t
i
c
al
t
ec
h
n
i
q
u
e.
K
e
y
w
o
r
d
s
:
6
-
D
hype
r
c
ha
oti
c
s
ys
tem
C
ha
os
s
ync
hr
oniza
ti
on
L
ya
punov
s
tabili
ty
theor
y
Nonlinea
r
c
ontr
ol
s
tr
a
tegy
S
e
lf
-
e
xc
it
e
d
a
tt
r
a
c
tor
Th
i
s
i
s
a
n
o
p
en
a
c
ces
s
a
r
t
i
c
l
e
u
n
d
e
r
t
h
e
CC
B
Y
-
SA
l
i
ce
n
s
e
.
C
or
r
e
s
pon
din
g
A
u
th
or
:
S
a
a
d
F
a
wz
i
AL
-
Az
z
a
wi,
De
pa
r
tm
e
nt
of
M
a
thema
ti
c
s
,
C
oll
e
ge
of
C
omput
e
r
S
c
ienc
e
a
nd
M
a
th
e
matics
,
Unive
r
s
it
y
of
M
os
ul,
M
os
ul,
I
r
a
q
.
E
mail:
s
a
a
d_f
a
wz
i78@yahoo.
c
om,
s
a
a
d_a
laz
a
wi@uomos
ul.
e
du.
iq
1.
I
NT
RODU
C
T
I
ON
I
n
r
e
c
e
nt
ye
a
r
s
,
the
dyna
mi
c
a
l
s
ys
tem
ha
s
a
tt
r
a
c
ted
s
igni
f
ica
nt
a
tt
e
nti
on
due
to
it
s
wide
s
pr
e
a
d
a
ppli
c
a
ti
ons
in
e
nginee
r
ing
a
nd
di
f
f
e
r
e
nt
s
c
ientif
ic
r
e
s
e
a
r
c
h
a
s
las
e
r
s
,
nonli
ne
a
r
ci
rcu
i
t
s
biol
ogica
l
[
1,
2
]
,
e
nginee
r
ing
[
3,
4]
a
nd
s
e
c
ur
e
c
omm
unica
ti
ons
[
5,
6
].
L
or
e
nz
s
ys
tem
is
the
f
i
r
s
t
phys
ica
l
a
nd
math
e
matica
l
model
of
a
c
ha
oti
c
s
ys
tem
c
ontains
r
e
a
l
va
r
iable
s
only
whic
h
dis
c
ove
r
e
d
in
1963
a
nd
ope
n
the
wa
y
to
f
ind
a
nother
c
ha
oti
c
s
ys
t
e
m
s
u
c
h
a
s
C
h
e
n
s
ys
tem,
Lu
s
ys
tem,
L
iu
s
ys
tem
a
nd
P
a
n
s
y
s
tem
[
7
-
9
]
.
E
a
c
h
s
ys
t
e
m
ha
s
a
3
-
D
of
dif
f
e
r
e
nti
a
l
e
qua
ti
ons
a
nd
jus
t
one
pos
it
ive
L
ya
punov
e
xpone
nt
[
10
].
One
im
por
tant
a
ppli
c
a
ti
on
in
the
f
ield
of
e
nginee
r
ing
is
s
e
c
ur
e
c
omm
unica
ti
on
i
.
e
.
,
the
mes
s
a
ge
s
whic
h
a
r
e
made
by
s
uc
h
s
im
ple
c
ha
oti
c
s
ys
tems
a
r
e
not
a
lwa
ys
s
a
f
e
[
6,
11,
12]
.
I
t
is
s
ugge
s
ted
that
thi
s
p
r
oblem
c
a
n
be
ove
r
c
ome
by
us
ing
higher
-
dim
e
ns
ional
hype
r
c
ha
oti
c
s
ys
tems
,
whic
h
ha
ve
incr
e
a
s
e
d
r
a
ndomn
e
s
s
a
nd
higher
unpr
e
dicta
bil
it
y
.
I
n
1979
,
R
ös
s
ler
dis
c
ove
r
s
t
he
f
i
r
s
t
4
-
D
hype
r
c
ha
oti
c
s
ys
tem
including
r
e
a
l
va
r
iable
s
wi
th
two
pos
it
ive
L
ya
pu
nov
e
xpone
nts
a
nd
f
oll
owe
d
to
dis
c
ove
r
a
nother
4
-
D,
a
s
we
ll
a
s
5
-
D
hype
r
c
ha
oti
c
w
it
h
th
r
e
e
pos
it
ive
L
ya
punov
e
xpon
e
nts
[
10
,
13
-
15]
a
nd
s
ome
other
s
ys
tems
,
ha
ve
be
e
n
r
e
ve
a
led.
T
he
d
yna
mi
c
a
l
s
ys
tems
with
higher
di
mens
ions
a
r
e
e
f
f
e
c
ti
ve
a
n
d
int
e
r
e
s
ti
ng
c
ompar
e
d
with
the
low
dim
e
ns
ions
[
16
-
18
]
.
I
n
2015
,
Ya
ng
e
t
a
l.
,
pr
opo
s
e
s
a
6
-
D
hype
r
c
ha
o
ti
c
s
ys
tem
including
r
e
a
l
va
r
ia
bles
a
nd
ha
s
f
our
pos
it
ive
L
ya
punov
e
xpone
nts
[
19
]
.
T
he
s
e
da
ys
,
the
s
ync
hr
oniza
ti
on
o
f
the
mentioned
s
ys
tems
witnes
s
e
d
lar
ge
a
tt
e
nti
on
by
r
e
s
e
a
r
c
he
r
s
be
c
a
us
e
of
it
s
im
po
r
tant
a
ppli
c
a
ti
ons
in
the
is
s
e
c
ur
e
c
omm
unica
ti
on
[
20
-
22]
.
M
a
ny
of
the
pa
pe
r
s
t
ha
t
r
e
l
a
te
to
thi
s
topi
c
a
r
e
incr
e
a
s
ing,
a
nd
numer
ous
r
e
s
e
a
r
c
h
de
voted
to
inves
ti
ga
ti
ng
C
S
of
high
-
dim
e
ns
ional
hype
r
c
ha
oti
c
s
ys
tems
ba
s
e
d
on
tr
a
dit
io
na
l
L
ya
pu
nov
s
tabili
ty
theor
y
[
23
-
2
5
]
.
L
ya
punov
s
tabili
ty
t
he
or
y
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
3
,
J
une
2020:
1483
-
1490
1484
e
xtens
ively
uti
li
z
e
d
in
the
phe
nomena
of
s
ync
h
r
oniza
ti
on
be
c
a
us
e
the
L
ya
punov
f
unc
ti
on
c
a
n
de
li
ve
r
a
c
c
ur
a
tely
a
nd
s
pe
e
d
da
ta
of
the
s
ys
tem
c
onve
r
ge
n
c
e
.
How
e
ve
r
,
L
ya
punov
f
unc
ti
on
in
s
ome
ti
me
is
i
nc
a
pa
ble
of
mee
ti
ng
the
c
onve
r
ge
nc
e
r
e
quir
e
ments
of
e
r
r
o
r
dyna
mi
c
s
s
ys
tem
owing
to
s
uf
f
e
r
s
f
r
om
it
s
dr
a
w
ba
c
ks
of
modi
f
ied
the
f
unc
ti
on
it
s
e
lf
.
T
o
a
c
hieve
s
ync
hr
oniza
ti
on
of
good
pe
r
f
or
manc
e
,
the
L
inea
r
iza
ti
o
n
tool
is
pr
e
f
e
r
r
e
d.
S
o
the
L
inea
r
i
z
a
ti
on
a
nd
nonli
ne
a
r
c
ontr
ol
s
tr
a
tegy
int
e
gr
a
ti
on
c
a
n
a
c
hieve
higher
pe
r
f
or
ma
nc
e
.
T
he
c
ontr
ibut
ions
o
f
thi
s
r
e
s
e
a
r
c
h
c
a
n
be
s
umm
a
r
iz
e
d
in
the
f
oll
owing
po
int
s
.
a.
C
ha
os
s
ync
hr
oniza
ti
on
be
twe
e
n
identica
l
6
-
D
hype
r
c
ha
oti
c
s
ys
tems
is
s
tudi
e
d
a
nd
us
e
d
to
f
ind
the
e
r
r
or
dyna
mi
c
s
be
twe
e
n
them
a
nd
it
s
s
e
c
ur
e
c
omm
unica
ti
on
is
then
p
r
e
s
e
nted
theor
e
ti
c
a
ll
y
.
b.
De
s
igns
of
th
r
e
e
dif
f
e
r
e
nt
c
o
ntr
oll
e
r
s
of
c
ompl
e
te
s
ync
hr
oniza
ti
on
a
r
e
done
by
a
nonli
ne
a
r
c
o
ntr
ol
s
tr
a
tegy
ba
s
e
d
on
the
L
ya
punov
s
tabili
ty
theor
y
,
L
i
ne
a
r
iza
ti
on
met
hod.
c.
C
ompar
e
be
twe
e
n
the
L
ya
punov
a
nd
L
inea
r
iza
ti
on
method
.
2.
S
YST
E
M
DE
S
CR
I
P
T
I
ON
T
he
L
or
e
nz
s
ys
tem
wa
s
the
f
ir
s
t
3
-
D
c
h
a
oti
c
s
y
s
tem
to
be
modele
d
a
nd
one
of
the
mos
t
wide
ly
s
tudi
e
d.
T
he
o
r
igi
na
l
s
ys
tem
wa
s
modi
f
ied
in
to
a
4
-
D
a
nd
5
-
D
hype
r
c
ha
oti
c
s
ys
tems
by
int
r
oduc
ing
a
li
ne
a
r
f
e
e
dba
c
k
c
ontr
oll
e
r
.
I
n
2015
,
Ya
ng
c
ons
tr
uc
ted
a
6
-
D
hype
r
c
ha
oti
c
s
ys
tem
whic
h
c
ontains
f
our
pos
it
ive
L
ya
punov
E
xpone
nts
1
=
1
.
0034
,
2
=
0
.
57515
,
3
=
0
.
32785
,
4
=
0
.
0
2
0
9
3
7
,
a
nd
two
ne
ga
ti
ve
L
ya
punov
E
xpone
nts
5
=
−
0
.
1
2
0
8
7
,
6
=
−
12
.
4713
.
T
he
6
-
D
s
ys
tem
w
hich
is
de
s
c
r
ibed
by
the
f
oll
owing
mathe
matica
l
f
or
m
[
1
9
]:
{
̇
1
=
(
2
−
1
)
+
4
̇
2
=
1
−
2
−
1
3
+
5
̇
3
=
−
3
+
1
2
̇
4
=
4
−
1
3
̇
5
=
−
2
̇
6
=
ℎ
6
+
2
(
1)
whe
r
e
1
,
2
,
3
,
4
,
5
,
6
a
r
e
r
e
a
l
s
tate
va
r
iable
s
a
nd
,
,
,
,
,
ℎ
,
a
r
e
a
ll
pos
it
iv
e
r
e
a
l
pa
r
a
mete
r
s
whic
h
e
qua
ls
(
10
,
8
/
3
,
28
,
2
,
8
.
4
,
1
,
1
)
r
e
s
pe
c
ti
ve
ly
.
T
his
s
ys
tem
is
r
ich
in
dyna
mi
c
pr
ope
r
ti
e
s
.
F
igu
r
e
1
(
a
)
s
hows
the
3
-
D
a
tt
r
a
c
tor
of
the
s
ys
tem
(
1
)
,
while
F
igu
r
e
1
(
b)
s
hows
the
2
-
D
a
tt
r
a
c
tor
of
the
s
a
me
s
ys
tem.
(
a
)
(
b)
F
igu
r
e
1
.
T
he
a
tt
r
a
c
tor
of
the
s
ys
tem
(
1
)
,
(
a
)
I
n
the
3
-
D
(
1
,
3
,
6
)
s
pa
c
e
,
(
b)
I
n
the
2
-
D
(
1
,
3
)
plane
3.
CHAOS
S
YN
CHRONI
Z
AT
I
ON
B
E
T
WE
E
N
T
WO
I
DE
NT
I
CA
L
L
ORE
NZ
S
YST
E
M
I
n
thi
s
s
e
c
ti
on,
two
s
ys
tems
a
r
e
ne
e
de
d,
the
f
ir
s
t
s
ys
tem
is
c
a
ll
e
d
the
d
r
ive
s
ys
tem
whic
h
r
e
pr
e
s
e
nts
the
pictur
e
or
mes
s
a
ge
inf
o
r
mation
will
be
s
e
nt
w
hil
e
the
s
e
c
ond
s
ys
tem
is
c
a
ll
e
d
r
e
s
pons
e
s
ys
tem
r
e
pr
e
s
e
nts
the
nois
e
that
f
oll
owe
d
thi
s
inf
or
mation
to
e
ns
ur
e
that
they
a
r
e
not
pe
ne
tr
a
ted.
As
s
ume
that
the
s
ys
te
m
(
1)
is
the
dr
ive
s
ys
tem
a
nd
c
a
n
be
wr
it
ten
a
s
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
C
haos
s
y
nc
h
r
oniz
ati
on
in
a
6
-
D
hy
pe
r
c
haoti
c
s
y
s
te
m
w
it
h
s
e
lf
-
e
x
c
it
e
d
att
r
ac
tor
(
A
hme
d
S
.
A
l
-
Obe
idi
)
1485
[
̇
1
̇
2
̇
3
̇
4
̇
5
̇
6
]
=
[
−
0
0
0
0
−
1
0
0
−
0
0
−
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
ℎ
]
⏟
[
1
2
3
4
5
6
]
+
[
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
]
⏟
[
−
1
3
1
2
−
1
3
]
⏟
(
2)
a
nd
the
pr
oduc
t
.
r
e
pr
e
s
e
nts
pa
r
a
mete
r
s
matr
ix
a
nd
nonli
ne
a
r
pa
r
t
o
f
the
s
ys
tem
(
1)
,
r
e
s
pe
c
ti
ve
ly.
W
hil
e
the
r
e
s
pons
e
s
ys
tem
is
a
s
f
oll
ows
:
[
̇
1
̇
2
̇
3
̇
4
̇
5
̇
6
]
=
1
[
1
2
3
4
5
6
]
+
(
1
[
−
1
3
1
2
−
1
3
]
⏟
1
+
[
1
2
3
4
5
6
]
)
(
3)
a
nd
let
=
[
1
,
2
,
3
,
4
,
5
,
6
]
is
the
nonli
ne
a
r
c
ontr
ol
ler
to
be
de
s
ig
ne
d.
T
he
s
ync
hr
on
iza
ti
on
e
r
r
o
r
dyna
mi
c
s
be
twe
e
n
the
6
-
D
hype
r
c
ha
oti
c
s
ys
tem
(
2
)
a
nd
s
ys
tem
(
3
)
is
de
f
ined
a
s
=
−
,
=
1
,
2
,
…
,
6
a
nd
s
a
ti
s
f
ied
that
,
l
im
→
∞
=
0
.
T
he
e
r
r
o
r
dyna
mi
c
s
is
c
a
lcula
te
d
a
s
the
f
oll
owing:
{
̇
1
=
(
2
−
1
)
+
4
+
1
̇
2
=
c
1
−
2
−
1
3
−
3
1
−
1
3
+
5
+
2
̇
3
=
−
b
3
+
1
2
+
2
1
+
1
2
+
3
̇
4
=
d
4
−
1
3
−
3
1
−
1
3
+
4
̇
5
=
−
2
+
5
̇
6
=
ℎ
6
+
2
+
6
(
4)
I
f
the
matr
ice
s
1
a
nd
1
a
s
1
=
a
nd
1
=
,
t
he
n
r
e
f
e
r
f
o
r
identica
l
s
ync
hr
oniza
ti
on
.
1
≠
or
1
≠
,
then
r
e
f
e
r
f
or
non
-
identica
l
s
ync
hr
oniza
ti
on
.
B
a
s
e
d
on
L
inea
r
iza
ti
on
method
,
T
he
s
ys
tem
(
4
)
i
s
uns
table
a
nd
the
c
ha
r
a
c
ter
is
ti
c
e
qua
ti
on
a
nd
e
ig
e
nva
lues
a
r
e
r
e
s
pe
c
ti
ve
ly
a
s
λ
6
+
32
3
λ
5
−
4069
15
λ
4
+
1658
15
λ
3
+
24004
15
λ
2
−
9496
5
λ
−
448
=
0
{
λ
1
=
2
λ
2
=
1
λ
3
=
−
8
/
3
λ
4
=
11
.
3659
−
8
.
10
−
9
λ
5
=
−
22
.
6916
−
3
.
9
2
8
2
0
3
2
3
0
1
0
−
9
λ
6
=
0
.
3257
+
9
.
9
2
8
2
0
3
2
3
0
1
0
−
9
Now
,
dif
f
e
r
e
nt
c
ont
r
oll
e
r
s
a
r
e
de
s
igned
ba
s
e
d
o
n
L
ya
punov
a
nd
L
inea
r
iza
ti
on
methods
a
nd
we
c
ompar
e
them.
T
he
or
e
m
1
.
I
f
the
c
ontr
ol
of
s
ys
tem
(
4)
is
de
s
ign
a
s
the
f
oll
owing:
{
1
=
4
(
3
−
1
)
−
2
(
a
+
−
3
)
2
=
−
6
3
=
−
2
1
4
=
3
(
1
+
1
)
−
3
4
5
=
−
2
(
1
−
)
−
5
6
=
−
2ℎ
6
(
5)
T
he
n
the
s
ys
tem
(
3)
c
a
n
be
f
oll
owe
d
by
the
s
ys
tem
(
2)
by
two
methods
.
P
r
oof
.
S
ubs
ti
tut
e
a
bove
c
ontr
ol
in
the
e
r
r
o
r
dyna
m
ics
s
ys
tem
(
4)
we
ha
ve
(
6
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
3
,
J
une
2020:
1483
-
1490
1486
{
̇
1
=
−
1
+
3
4
−
2
+
3
2
̇
2
=
c
1
−
2
−
1
3
−
3
1
−
1
3
+
5
−
6
̇
3
=
−
b
3
+
1
2
+
1
2
̇
4
=
−
2d
4
−
3
1
̇
5
=
−
2
−
5
̇
6
=
2
−
ℎ
6
(
6)
I
n
the
f
ir
s
t
method
(
L
inea
r
iza
ti
on
method
)
,
t
he
c
h
a
r
a
c
ter
is
ti
c
e
qua
ti
on
a
nd
e
igenva
lues
a
s
λ
6
+
32
3
λ
5
+
2488
3
λ
4
+
20696
3
λ
3
+
59225
3
λ
2
+
66172
3
λ
+
25184
3
=
0
{
λ
1
=
−
4
λ
2
=
−
1
λ
3
=
−
1
λ
4
=
−
8
/
3
λ
5
=
−
1
+
√
786
λ
6
=
−
1
−
√
786
All
r
e
a
l
pa
r
ts
o
f
e
igenva
lues
a
r
e
ne
ga
ti
ve
,
t
he
li
ne
a
r
iza
ti
on
method
is
r
e
a
li
z
e
d
the
c
ha
os
s
ync
hr
oniza
ti
on
be
twe
e
n
s
ys
tem
(
2)
a
nd
s
ys
tem
(
3
)
.
I
f
the
L
ya
punov
f
unc
ti
on
is
c
ons
tr
uc
t
e
d
a
s
(
7)
.
(
)
=
1
2
∑
2
6
=
1
=
,
=
(
0
.
5
,
0
.
5
,
0
.
5
,
0
.
5
,
0
.
5
,
0
.
5
)
(
7)
T
he
de
r
ivative
o
f
the
a
bove
f
unc
ti
on
(
)
is
̇
(
)
=
1
̇
1
+
2
̇
2
+
3
̇
3
+
4
̇
4
+
5
̇
5
+
6
̇
6
̇
(
)
=
1
(
−
1
+
3
4
−
2
+
3
2
)
+
2
(
1
−
2
−
1
3
−
3
1
−
1
3
+
5
−
6
)
+
3
(
−
b
3
+
1
2
+
1
2
)
+
4
(
−
2d
4
−
3
1
)
+
5
(
−
2
−
5
)
+
6
(
2
−
ℎ
6
)
̇
(
)
=
−
1
2
−
2
2
−
3
2
−
2
4
2
−
5
2
−
ℎ
6
2
=
−
(
8)
whe
r
e
=
(
,
1
,
,
2
,
1
,
ℎ
)
,
s
o
>
0
.
C
ons
e
que
ntl
y,
̇
(
)
is
ne
ga
ti
ve
de
f
ini
te
on
6
.
T
he
nonli
ne
a
r
c
ontr
oll
e
r
is
s
uit
a
ble
a
nd
the
c
ompl
e
te
s
ync
hr
o
niz
a
ti
on
is
a
c
hieve
d.
Now
,
we
will
take
the
ini
ti
a
l
v
a
lues
a
s
(
1
,
0
,
2
,
4
,
1
,
−
1
)
a
nd
(
−
8
,
−
7
,
−
15
,
12
,
20
,
1
)
to
il
lus
tr
a
te
the
c
ompl
e
te
s
ync
hr
oniza
ti
on
that
ha
ppe
ne
d
be
twe
e
n
(
2)
a
nd
(
3)
numer
ica
ll
y.
F
ig
u
r
e
2
s
hows
ve
r
if
y
thes
e
r
e
s
ult
s
numer
ica
ll
y.
F
igur
e
2
.
C
ompl
e
te
s
ync
hr
oniza
ti
on
be
twe
e
n
s
ys
tems
(
2)
a
nd
(
3)
with
c
ont
r
ol
(
5)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
C
haos
s
y
nc
h
r
oniz
ati
on
in
a
6
-
D
hy
pe
r
c
haoti
c
s
y
s
te
m
w
it
h
s
e
lf
-
e
x
c
it
e
d
att
r
ac
tor
(
A
hme
d
S
.
A
l
-
Obe
idi
)
1487
T
he
or
e
m
2
.
I
f
the
non
li
ne
a
r
c
ont
r
ol
of
e
r
r
or
dyna
mi
c
a
l
s
ys
tem
(
4)
is
de
s
igned
(
9)
.
{
1
=
−
2
−
2
3
+
3
(
4
+
2
)
2
=
−
1
−
6
3
=
1
4
4
=
1
(
3
−
)
−
2
4
5
=
−
5
6
=
−
2ℎ
6
(
9)
T
he
n
the
s
ys
t
e
m
(
3)
c
a
n
be
f
oll
owe
d
by
the
s
ys
tem
(
2)
by
two
methods
.
P
r
oof
.
F
r
o
m
the
a
bove
c
ontr
ol
(
9)
with
the
e
r
r
o
r
s
y
s
tem
(
4)
,
we
ge
t
(
10)
.
{
̇
1
=
2
−
1
+
4
−
2
−
2
3
+
3
4
+
3
2
̇
2
=
c
1
−
2
−
1
3
−
3
1
−
1
3
+
5
−
1
−
6
̇
3
=
−
3
+
1
2
+
2
1
+
1
2
+
1
4
̇
4
=
−
4
−
3
1
−
1
3
−
1
̇
5
=
−
2
−
5
̇
6
=
2
−
ℎ
6
(
10)
B
a
s
e
d
on
the
f
ir
s
t
method
(
L
inea
r
iza
ti
on
method)
,
t
he
c
ha
r
a
c
ter
is
ti
c
e
qua
ti
on
a
nd
e
igenva
lues
a
s
:
λ
6
+
53
3
λ
5
+
2172
5
λ
4
+
38594
15
λ
3
+
91112
15
λ
2
+
93856
15
λ
+
35072
15
=
0
{
λ
1
=
−
1
λ
2
=
−
8
/
3
λ
3
=
−
1
.
3438
λ
4
=
−
1
.
9026
λ
5
=
−
5
.
3768
+
17
.
7207
λ
6
=
−
5
.
3768
−
17
.
7207
a
ll
r
e
a
l
pa
r
ts
of
e
igenva
lues
a
r
e
ne
ga
ti
ve
.
T
he
li
ne
a
r
iza
ti
on
method
is
s
uc
c
e
e
de
d
to
a
c
hieve
c
ompl
e
te
s
ync
hr
oniza
ti
on.
In
L
ya
punov
a
ppr
oa
c
h,
the
L
ya
punov
f
unc
ti
on
is
take
n
a
s
the
s
a
me
f
o
r
m
in
theor
e
m1,
the
de
r
ivative
L
ya
punov
f
unc
ti
on
with
c
ontr
ol
(
9)
be
c
omes
̇
(
)
=
−
1
2
−
2
2
−
3
2
−
4
2
−
5
2
−
ℎ
6
2
+
1
4
(
1
−
)
+
2
5
(
1
−
)
=
−
1
(
11)
w
he
r
e
1
=
[
0
0
−
(
1
−
)
/
2
0
0
0
1
0
0
−
(
1
−
)
/
2
0
0
0
0
0
0
−
(
1
−
)
/
2
0
0
0
0
0
−
(
1
−
)
/
2
0
0
1
0
0
0
0
0
0
ℎ
]
Note
that
1
is
not
a
diagona
l
matr
ix.
I
f
a
ll
the
f
oll
ow
ing
f
ive
inequa
li
ti
e
s
a
r
e
s
a
ti
s
f
ied,
then
the
1
is
pos
it
ive
de
f
ini
te:
{
1
.
>
0
2
.
>
0
3
.
ℎ
>
0
4
.
(
−
(
1
−
)
2
4
)
>
0
5
.
(
(
1
−
(
1
−
)
2
4
)
−
(
1
−
)
2
4
(
1
−
(
1
−
)
2
4
)
)
>
0
(
12)
F
if
th
inequa
li
ty
is
not
c
or
r
e
c
t
wi
th
given
pa
r
a
met
e
r
s
.
T
he
r
e
f
o
r
e
,
thi
s
c
ontr
ol
is
f
a
il
e
d
.
If
upda
te
the
matr
ix
with
the
s
a
me
c
ontr
ol
a
s
:
1
=
(
1
2
⁄
,
1
2
⁄
,
1
2
⁄
,
1
4
⁄
,
5
/
84
,
1
)
(
13)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
3
,
J
une
2020:
1483
-
1490
1488
T
he
n,
the
de
r
ivative
o
f
L
ya
punov
f
unc
ti
on
a
s
:
̇
(
)
=
−
10
1
2
−
2
2
−
8
3
3
2
−
4
2
−
5
42
5
2
−
6
2
=
−
2
(
14)
whe
r
e
2
=
(
10
,
1
,
8
/
3
,
1
,
5
/
42
,
1
)
is
a
pos
it
ive
de
f
ini
te
.
F
ig
ur
e
3
s
hows
ve
r
if
y
thes
e
r
e
s
ult
s
numer
ic
a
ll
y.
F
igur
e
3
.
C
ompl
e
te
s
ync
hr
oniza
ti
on
be
twe
e
n
s
ys
tems
(
2)
a
nd
(
3)
with
c
ont
r
ol
(
9)
T
he
or
e
m
3
.
I
f
the
nonli
ne
a
r
c
ont
r
ol
of
e
r
r
or
dyna
mi
c
a
l
s
ys
tem
(
4)
is
de
s
igned
a
s
:
{
1
=
−
2
−
(
5
+
2
)
2
=
−
6
+
3
1
3
=
4
(
1
+
1
)
−
2
1
4
=
−
1
−
2
4
+
3
1
5
=
−
2
−
5
+
(
2
1
+
2
)
6
=
−
2ℎ
6
(
15)
then
the
s
ys
tem
(
3)
c
a
n
be
f
o
ll
owe
d
by
the
s
ys
tem
(
2)
by
li
ne
a
r
iza
ti
on
method
only.
P
r
oof
.
R
e
wr
it
e
s
ys
tem
(
4)
with
c
ontr
ol
(
15)
a
s
f
oll
ows
(
16)
.
{
̇
1
=
−
1
+
4
−
2
−
5
̇
2
=
c
1
−
2
−
1
3
−
1
3
+
5
−
6
̇
3
=
−
b
3
+
1
2
+
1
2
+
1
4
+
1
4
̇
4
=
−
d
4
−
1
3
−
1
3
−
1
̇
5
=
−
2
−
5
+
2
1
̇
6
=
2
−
ℎ
6
(
16)
B
a
s
e
d
on
the
L
ya
punov
s
tabili
ty
theor
y,
we
obtain
̇
(
)
=
−
1
2
−
2
2
−
3
2
−
4
2
−
5
2
−
ℎ
6
2
+
1
5
(
2
−
)
=
−
3
(
17)
w
he
r
e
3
=
[
0
0
0
(
−
2
)
/
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
−
(
−
2
)
/
2
0
0
0
1
0
0
0
0
0
0
ℎ
]
(
18)
S
o
3
is
not
a
diagona
l
matr
ix
.
T
he
ne
c
e
s
s
a
r
y
c
ondit
ions
to
make
3
is
pos
it
ive
de
f
ini
te
,
the
f
oll
ow
ing
inequa
li
ti
e
s
mus
t
hold
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
C
haos
s
y
nc
h
r
oniz
ati
on
in
a
6
-
D
hy
pe
r
c
haoti
c
s
y
s
te
m
w
it
h
s
e
lf
-
e
x
c
it
e
d
att
r
ac
tor
(
A
hme
d
S
.
A
l
-
Obe
idi
)
1489
{
1
.
>
0
2
.
>
0
3
.
>
0
4
.
ℎ
>
0
5
.
>
(
−
2
)
2
4
(
19)
Note
a
ll
inequa
li
ti
e
s
a
r
e
r
e
a
li
z
e
d
e
x
c
e
pt
the
f
i
f
th
inequa
li
ty.
S
o
,
the
matr
ix
3
is
a
ne
ga
ti
ve
de
f
ini
ti
on,
a
nd
f
a
il
e
d
to
a
c
hieve
c
ompl
e
te
s
ync
hr
o
niza
ti
on.
T
he
r
e
f
or
e
mod
if
ied
the
matr
ix
a
s
f
oll
ows
:
{
3
,
1
=
(
21
/
25
,
1
/
2
,
1
/
2
,
1
/
2
,
1
/
2
,
1
/
2
)
3
,
2
=
(
1
/
2
,
1
/
2
,
1
/
2
,
1
/
2
,
2
5
/
84
,
1
2
⁄
)
3
,
3
=
(
1
/
20
,
1
/
2
,
1
/
2
,
1
/
2
,
5
/
1
6
8
,
1
2
⁄
)
a
ll
the
a
bove
matr
ice
s
a
r
e
not
diagona
l
3
,
ther
e
f
or
e
L
ya
punov
method
f
a
il
e
d.
B
a
s
e
d
on
L
inea
r
i
z
a
ti
on
method,
the
c
ha
r
a
c
ter
is
ti
c
e
qua
ti
on
a
nd
e
igenva
lue
s
as
λ
6
+
53
3
λ
5
+
1054
λ
4
+
34142
5
λ
3
+
83193
5
λ
2
+
53173
3
λ
+
35784
5
=
0
{
λ
1
=
−
8
/
3
λ
2
=
−
1
.
9967
λ
3
=
−
1
.
109
7
−
0
.
4060
λ
4
=
−
1
.
1097
+
0
.
4060
λ
5
=
−
5
.
3920
−
30
.
5554
λ
6
=
−
5
.
3920
+
30
.
5554
Note
that
a
ll
e
igenva
lues
with
ne
ga
ti
ve
r
e
a
l
pa
r
ts
,
a
nd
thus
the
L
inea
r
iza
ti
on
method
ha
s
s
uc
c
e
e
de
d
in
a
c
hieving
c
ompl
e
te
s
ync
hr
oniza
ti
on
be
twe
e
n
s
ys
tems
(
2)
a
nd
(
3)
without
a
ny
upda
te
c
ompar
e
d
to
the
L
ya
punov
method
a
nd
thus
the
p
r
oof
ha
s
be
e
n
c
o
mpl
e
ted.
T
he
s
e
r
e
s
ult
s
a
r
e
jus
ti
f
ied
numer
ica
ll
y
in
F
ig
ur
e
4.
F
igur
e
4
.
C
ompl
e
te
s
ync
hr
oniza
ti
on
be
twe
e
n
s
ys
tems
(
2)
a
nd
(
3)
with
c
ont
r
ol
(
15)
4.
CONC
L
USI
ON
I
n
thi
s
pa
pe
r
,
c
ompl
e
te
s
ync
hr
oniza
ti
on
of
a
6
-
D
hype
r
c
ha
oti
c
s
ys
tem
with
a
s
e
lf
-
e
xc
it
e
d
a
tt
r
a
c
tor
is
pr
opos
e
d.
ba
s
e
d
on
nonli
ne
a
r
c
ontr
ol
s
tr
a
tegy
a
nd
two
a
na
lyt
ica
l
methods
;
f
ir
s
t
is
L
ya
punov's
,
a
nd
th
e
s
e
c
ond
is
the
L
inea
r
iza
ti
on
method.
T
h
r
ough
thes
e
two
a
ppr
oa
c
he
s
we
ha
ve
f
ound
the
di
f
f
e
r
e
nc
e
be
twe
e
n
t
he
m
a
nd
wha
t
is
the
a
ppr
opr
iate
method
in
e
a
c
h
a
ppr
oa
c
h
f
or
a
c
hieving
c
ompl
e
te
s
ync
hr
oniza
ti
on
a
nd
thus
we
s
howe
d
the
be
s
t
wa
y
obs
e
r
ve
d
that
the
L
inea
r
iza
ti
on
meth
od
doe
s
not
ne
e
d
to
a
a
uxil
iar
y
f
unc
ti
on
or
modi
f
ying
thi
s
f
unc
ti
on
a
s
a
method
L
ya
punov.
T
hus
the
li
ne
a
r
iza
ti
on
method
is
be
tt
e
r
than
the
L
ya
punov
m
e
thod
in
a
c
hieving
the
de
s
ir
e
d
one
.
Nume
r
ica
l
r
e
s
ult
s
ha
ve
be
e
n
f
ound
to
be
the
s
a
me
r
e
s
ult
s
a
s
we
pr
opos
e
d.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
3
,
J
une
2020:
1483
-
1490
1490
AC
KNOWL
E
DGE
M
E
NT
S
T
he
a
uthor
s
a
r
e
ve
r
y
gr
a
tef
ul
to
Unive
r
s
it
y
of
M
os
ul/
C
oll
e
ge
of
C
omput
e
r
S
c
ienc
e
s
a
nd
M
a
thema
ti
c
s
f
or
their
p
r
ovided
f
a
c
il
it
ies
,
whic
h
he
lped
to
im
p
r
ove
the
qua
li
ty
of
thi
s
wor
k
.
RE
F
E
RE
NC
E
S
[1
]
S.
V
ai
d
y
an
a
t
h
a
n
,
et
al
.
,
“A
N
e
w
Bi
o
l
o
g
i
ca
l
Sn
a
p
O
s
ci
l
l
at
o
r:
It
s
Mo
d
el
l
i
n
g
,
A
n
al
y
s
i
s
,
Si
m
u
l
a
t
i
o
n
s
an
d
C
i
r
cu
i
t
D
es
i
g
n
,
”
In
t
e
r
n
a
t
i
o
n
a
l
Jo
u
r
n
a
l
o
f
S
i
m
u
l
a
t
i
o
n
a
n
d
P
r
o
ce
s
s
M
o
d
e
l
l
i
n
g
,
v
o
l
.
1
3
,
n
o
.
5
,
p
p
.
4
1
9
-
4
3
2
,
J
an
2
0
1
8
.
[2
]
Z
.
N
.
A
l
-
K
h
at
ee
b
an
d
M.
F.
J
a
d
er,
“E
n
cry
p
t
i
o
n
an
d
H
i
d
i
n
g
T
ex
t
U
s
i
n
g
D
N
A
Co
d
i
n
g
an
d
H
y
p
erc
h
ao
t
i
c
S
y
s
t
e
m,
”
In
d
o
n
e
s
i
a
n
J
o
u
r
n
a
l
o
f
E
l
ec
t
r
i
ca
l
E
n
g
i
n
ee
r
i
n
g
a
n
d
C
o
m
p
u
t
e
r
S
ci
e
n
ce
,
v
o
l
.
1
9
,
n
o
.
2
,
A
u
g
2
0
2
0
.
[3
]
K
.
A
.
A
b
ed
a
n
d
A
.
A
.
A
h
mad
,
“T
h
e
Bes
t
Paramet
ers
S
el
ect
i
o
n
U
s
i
n
g
P
s
o
A
l
g
o
r
i
t
h
m
t
o
So
l
v
i
n
g
Fo
r
I
t
o
Sy
s
t
e
m
b
y
N
ew
I
t
erat
i
v
e
T
ec
h
n
i
q
u
e,
”
In
d
o
n
es
i
a
n
J
o
u
r
n
a
l
o
f
E
l
ec
t
r
i
ca
l
E
n
g
i
n
ee
r
i
n
g
a
n
d
C
o
m
p
u
t
er
S
c
i
en
ce
,
v
o
l
.
1
8
,
n
o
.
3
,
p
p
.
1
6
3
8
-
1
6
4
5
,
J
u
n
e
2
0
2
0
.
[4
]
A.
F.
,
Q
as
i
m
,
B.
J
.
Sal
i
m,
“A
p
p
l
i
cat
i
o
n
N
e
w
It
era
t
i
v
e
Met
h
o
d
fo
r
S
o
l
v
i
n
g
Mo
d
i
f
i
ed
K
o
r
t
ew
e
g
-
D
e
v
ri
e
s
(MK
d
V
)
Sy
s
t
em
Fr
o
m
T
h
ree
E
q
u
a
t
i
o
n
s
,
”
Jo
u
r
n
a
l
o
f
A
d
va
n
c
ed
R
es
e
a
r
c
h
i
n
D
y
n
a
m
i
c
a
l
a
n
d
Co
n
t
r
o
l
S
ys
t
em
s
,
v
o
l
.
1
1
pp.
1
-
7
,
2
0
1
9
.
[5
]
M.
E
.
Sah
i
n
,
et
al
.
"
A
p
p
l
i
ca
t
i
o
n
an
d
Mo
d
e
l
i
n
g
o
f
a
N
o
v
el
4
D
Memri
s
t
i
v
e
Ch
ao
t
i
c
Sy
s
t
em
fo
r
Co
mm
u
n
i
c
at
i
o
n
Sy
s
t
em
s
.
"
Ci
r
c
u
i
t
s
,
S
y
s
t
e
m
s
,
a
n
d
S
i
g
n
a
l
P
r
o
ce
s
s
i
n
g
,
1
-
3
0
J
an
u
ary
2
0
2
0
.
[6
]
A
h
ma
d
,
Is
rar,
et
al
.
,
"
G
l
o
b
al
F
i
n
i
t
e
-
T
i
me
Mu
l
t
i
-
Sw
i
t
ch
i
n
g
Sy
n
c
h
ro
n
i
za
t
i
o
n
o
f
E
x
t
ern
a
l
l
y
Pert
u
rb
e
d
Ch
a
o
t
i
c
O
s
c
i
l
l
at
o
rs
"
Ci
r
c
u
i
t
s
,
S
y
s
t
e
m
s
,
a
n
d
S
i
g
n
a
l
P
r
o
ce
s
s
i
n
g
,
v
o
l
.
3
7
,
n
o
.
1
2
,
p
p
.
5
2
5
3
-
5
2
7
8
,
D
ecemb
er
2
0
1
8
.
[7
]
H
.
K
.
Ch
e
n
,
“G
l
o
b
al
Ch
a
o
s
S
y
n
c
h
ro
n
i
za
t
i
o
n
o
f
N
ew
Ch
ao
t
i
c
Sy
s
t
em
s
v
i
a
N
o
n
l
i
n
ear
C
o
n
t
ro
l
,
”
Ch
a
o
s
,
S
o
l
i
t
o
n
s
a
n
d
F
r
a
ct
a
l
s
,
v
o
l
.
2
3
,
n
o
.
4
,
p
p
.
1
2
4
5
-
1
2
5
1
,
Feb
ru
ar
y
2
0
0
5
.
[8
]
S.
F.
A
l
-
A
zzaw
i
,
“
St
a
b
i
l
i
t
y
a
n
d
B
i
fu
rca
t
i
o
n
o
f
Pan
Ch
a
o
t
i
c
Sy
s
t
em
b
y
U
s
i
n
g
R
o
u
t
h
-
H
u
r
w
i
t
z
an
d
G
ard
an
M
e
t
h
o
d
,”
A
p
p
l
i
ed
M
a
t
h
em
a
t
i
cs
a
n
d
Co
m
p
u
t
a
t
i
o
n
,
v
o
l
.
2
1
9
,
n
o
.
3
,
p
p
.
1
1
4
4
-
1
1
5
2
,
O
ct
o
b
er
2
0
1
2
.
[9
]
J
.
H
.
Park
,
“
Ch
ao
s
Sy
n
ch
r
o
n
i
zat
i
o
n
o
f
a
Ch
ao
t
i
c
Sy
s
t
e
m
v
i
a
N
o
n
l
i
n
ear
Co
n
t
r
o
l
,”
Ch
a
o
s
S
o
l
i
t
o
n
s
F
r
a
c
t
a
l
s
,
v
o
l
.
25
,
n
o
.
3
,
p
p
.
5
7
9
-
5
8
4
,
2
0
0
5
.
[1
0
]
S.
F.
A
l
-
A
zza
w
i
a
n
d
M.
M.
A
zi
z,
“
Ch
ao
s
Sy
n
ch
r
o
n
i
zat
i
o
n
o
f
N
o
n
l
i
n
ear
D
y
n
am
i
cal
S
y
s
t
ems
v
i
a
a
N
o
v
el
A
n
a
l
y
t
i
cal
A
p
p
ro
ac
h
,”
A
l
ex
a
n
d
r
i
a
E
n
g
i
n
ee
r
i
n
g
J
o
u
r
n
a
l
,
v
o
l
.
57
,
n
o
.
4
,
p
p
.
3
4
9
3
-
3
5
0
0
,
D
ecem
b
er
2
0
1
8
.
[1
1
]
M.
M.
A
zi
z
an
d
S.
F.
A
l
-
A
zzaw
i
,
“
A
n
t
i
-
S
y
n
ch
r
o
n
i
zat
i
o
n
o
f
N
o
n
l
i
n
ear
D
y
n
ami
ca
l
Sy
s
t
em
s
Bas
e
d
o
n
G
ard
a
n
o
’s
M
et
h
o
d
,
”
O
p
t
i
k
,
v
o
l
.
1
3
4
,
p
p
.
1
0
9
-
1
2
0
,
A
p
r
i
l
2
0
1
7
.
[1
2
]
M.
M.
A
zi
z
an
d
S.
F.
A
l
-
A
zzaw
i
,
“
H
y
b
ri
d
Ch
ao
s
Sy
n
c
h
ro
n
i
za
t
i
o
n
B
et
w
e
en
T
w
o
D
i
ffere
n
t
H
y
p
erc
h
ao
t
i
c
Sy
s
t
e
ms
v
i
a
T
w
o
A
p
p
ro
ac
h
es
,”
O
p
t
i
k
,
v
o
l
.
1
3
8
,
p
p
.
3
2
8
-
3
4
0
,
J
u
n
2
0
1
7
.
[1
3
]
Z
.
Sh
.
A
l
-
T
a
l
i
b
a
n
d
S.
F.
A
L
-
A
zzaw
i
,
“Pro
j
ect
i
v
e
S
y
n
c
h
r
o
n
i
zat
i
o
n
fo
r
4
D
H
y
p
erc
h
ao
t
i
c
S
y
s
t
em
Ba
s
ed
o
n
A
d
ap
t
i
v
e
N
o
n
l
i
n
ear
Co
n
t
ro
l
St
rat
eg
y
,
”
In
d
o
n
es
i
a
n
Jo
u
r
n
a
l
o
f
E
l
ect
r
i
ca
l
E
n
g
i
n
ee
r
i
n
g
a
n
d
Co
m
p
u
t
er
S
c
i
en
ce
,
v
o
l
.
1
9
,
n
o
.
2
,
A
u
g
2
0
2
0
.
[1
4
]
R.
H
ao
,
et
al
.
,
“
Res
earch
o
n
4
-
d
i
me
n
s
i
o
n
al
Sy
s
t
em
s
w
i
t
h
o
u
t
E
q
u
i
l
i
b
ri
a
w
i
t
h
A
p
p
l
i
cat
i
o
n
,”
TE
LKO
M
NI
KA
Tel
eco
m
m
u
n
i
ca
t
i
o
n
Co
m
p
u
t
i
n
g
E
l
ect
r
o
n
i
c
s
a
n
d
Co
n
t
r
o
l
,
v
o
l
.
16
,
n
o
.
2
,
p
p
.
8
1
1
-
8
2
6
,
A
p
ri
l
2
0
1
8
.
[1
5
]
Y
.
D
.
Ch
u
,
et
a
l
.
,
“
Fu
l
l
St
a
t
e
H
y
b
r
i
d
Pr
o
j
ec
t
i
v
e
Sy
n
ch
r
o
n
i
zat
i
o
n
i
n
H
y
p
erch
ao
t
i
c
Sy
s
t
em
s
,”
Ch
a
o
s
S
o
l
i
t
o
n
s
F
r
a
ct
a
l
s
,
v
o
l
.
42
,
n
o
.
3
,
p
p
.
1
5
0
2
-
1
5
1
0
,
N
o
v
emb
er
2
0
0
9
.
[1
6
]
S.
Y
.
A
l
-
h
a
y
a
l
i
a
n
d
S.
F.
A
L
-
A
zza
w
i
,
“A
n
O
p
t
i
mal
N
o
n
l
i
n
ear
C
o
n
t
ro
l
fo
r
A
n
t
i
-
S
y
n
c
h
ro
n
i
za
t
i
o
n
o
f
Rab
i
n
o
v
i
c
h
H
y
p
erch
a
o
t
i
c
Sy
s
t
em,
”
In
d
o
n
e
s
i
a
n
J
o
u
r
n
a
l
o
f
E
l
ec
t
r
i
ca
l
E
n
g
i
n
eer
i
n
g
a
n
d
C
o
m
p
u
t
er
S
ci
e
n
ce
,
v
o
l
.
1
9
,
n
o
.
1
,
pp.
3
7
9
-
3
8
6
,
J
u
l
y
2
0
2
0
.
[1
7
]
M.
M.
A
zi
z
an
d
S.
F.
A
l
-
A
zza
w
i
,
“
S
o
me
Pro
b
l
em
s
o
f
Feed
b
ac
k
Co
n
t
r
o
l
St
rat
e
g
i
e
s
an
d
It
s
T
rea
t
men
t
,”
Jo
u
r
n
a
l
o
f
M
a
t
h
e
m
a
t
i
c
s
R
es
e
a
r
c
h
,
v
o
l
.
9
,
n
o
.
1
,
p
p
.
39
-
49
,
2
0
1
7
.
[1
8
]
M.
Sri
v
as
t
av
a,
e
t
al
.,
“
A
n
t
i
-
Sy
n
ch
r
o
n
i
za
t
i
o
n
b
et
w
een
I
d
en
t
i
cal
a
n
d
N
o
n
-
i
d
en
t
i
ca
l
Fract
i
o
n
al
-
O
r
d
er
Ch
a
o
t
i
c
Sy
s
t
ems
U
s
i
n
g
A
ct
i
v
e
C
o
n
t
ro
l
Met
h
o
d
,
”
No
n
l
i
n
e
a
r
D
yn
a
m
i
cs
,
v
o
l
.
76
,
n
o
.
2
,
p
p
.
9
0
5
-
9
1
4
,
D
ecemb
er
2
0
1
3
.
[1
9
]
Q
.
Y
an
g
,
et
al
.,
“
A
N
ew
6
D
H
y
p
erch
a
o
t
i
c
Sy
s
t
em
w
i
t
h
Fo
u
r
Po
s
i
t
i
v
e
L
y
a
p
u
n
o
v
E
x
p
o
n
en
t
s
Co
i
n
e
d
,”
In
t
er
n
a
t
i
o
n
a
l
Jo
u
r
n
a
l
o
f
B
i
f
u
r
c
a
t
i
o
n
a
n
d
Ch
a
o
s
,
v
o
l
.
2
5,
n
o
.
4
,
p
p
.
1
5
5
0
0
6
1
-
1
5
5
0
0
7
9
,
2
0
1
5
.
[2
0
]
S.
F.
A
l
-
A
zzaw
i
an
d
M.
M.
A
zi
z,
“
St
ra
t
eg
i
es
o
f
L
i
n
ear
Feed
b
ack
C
o
n
t
ro
l
an
d
i
t
s
C
l
as
s
i
f
i
ca
t
i
o
n
,
”
TE
LK
O
M
NI
KA
Tel
eco
m
m
u
n
i
ca
t
i
o
n
Co
m
p
u
t
i
n
g
E
l
ect
r
o
n
i
c
s
a
n
d
Co
n
t
r
o
l
,
vol.
17
,
n
o
.
4
,
p
p
.
1
9
3
1
-
1
9
4
0
,
A
u
g
u
s
t
2
0
1
9
.
[2
1
]
A
.
S.
Al
-
O
b
e
i
d
i
an
d
S.
F.
A
l
-
A
zzaw
i
,
“
Co
mp
l
e
t
e
Sy
n
ch
ro
n
i
za
t
i
o
n
o
f
a
N
o
v
el
6
-
D
H
y
p
erch
a
o
t
i
c
L
o
ren
z
Sy
s
t
em
w
i
t
h
K
n
o
w
n
P
aramet
er
s
,”
In
t
e
r
n
a
t
i
o
n
a
l
Jo
u
r
n
a
l
o
f
E
n
g
i
n
ee
r
i
n
g
&
Tech
n
o
l
o
g
y
(U
A
E
)
,
v
o
l
.
7
,
n
o
.
4
,
pp.
5
3
4
5
-
5
3
4
9
,
2
0
1
8
.
[2
2
]
A
.
S.
Al
-
O
b
e
i
d
i
an
d
S.
F.
A
l
-
A
zzaw
i
,
“
Pro
j
ec
t
i
v
e
S
y
n
c
h
ro
n
i
za
t
i
o
n
fo
r
a
C
l
as
s
o
f
6
-
D
H
y
p
erc
h
ao
t
i
c
L
o
r
en
z
S
y
s
t
em
,”
I
n
d
o
n
e
s
i
a
n
J
o
u
r
n
a
l
o
f
E
l
ect
r
i
ca
l
E
n
g
i
n
eer
i
n
g
a
n
d
C
o
m
p
u
t
er
S
ci
e
n
ce
,
v
o
l
.
16
,
n
o
.
2
,
p
p
.
6
9
2
-
700
,
N
o
v
emb
er
2
0
1
9
.
[2
3
]
Z
.
Sh
.
A
l
-
T
al
i
b
an
d
S.
F.
A
L
-
A
zzaw
i
,
“
Pro
j
ec
t
i
v
e
an
d
H
y
b
ri
d
P
ro
j
ect
i
v
e
S
y
n
ch
r
o
n
i
za
t
i
o
n
o
f
4
-
D
H
y
p
erch
a
o
t
i
c
S
y
s
t
em
v
i
a
N
o
n
l
i
n
ear
C
o
n
t
ro
l
l
er
S
t
ra
t
eg
y
,”
TE
LKO
M
NIKA
Tel
eco
m
m
u
n
i
ca
t
i
o
n
Co
m
p
u
t
i
n
g
E
l
ect
r
o
n
i
c
s
a
n
d
Co
n
t
r
o
l
,
v
o
l
.
18
,
n
o
.
2
,
p
p
.
1
0
1
2
-
1
0
2
0
,
A
p
r
i
l
2
0
2
0
.
[2
4
]
Z
.
Sh
.
A
l
-
T
al
i
b
an
d
S.
F.
A
L
-
A
zzaw
i
,
“
Pro
j
ec
t
i
v
e
an
d
H
y
b
ri
d
P
ro
j
ect
i
v
e
S
y
n
ch
r
o
n
i
za
t
i
o
n
o
f
4
-
D
H
y
p
erch
a
o
t
i
c
S
y
s
t
em
v
i
a
N
o
n
l
i
n
ear
C
o
n
t
ro
l
l
er
S
t
ra
t
eg
y
,”
TE
LKO
M
NIKA
Tel
eco
m
m
u
n
i
ca
t
i
o
n
Co
m
p
u
t
i
n
g
E
l
ect
r
o
n
i
c
s
a
n
d
Co
n
t
r
o
l
,
v
o
l
.
18
,
n
o
.
2
,
p
p
.
1
0
1
2
-
1
0
2
0
,
A
p
r
i
l
2
0
2
0
.
[2
5
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