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c
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s
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K
ey
w
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r
d
s
:
Ab
s
o
lu
te
C
h
ar
ac
ter
is
ti
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p
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ly
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o
m
ial
Hig
h
er
-
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r
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er
d
y
n
am
ics
M
ar
g
in
al
s
tab
ilit
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Stab
ilit
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b
o
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r
ies
T
h
is i
s
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c
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rticle
u
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d
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CC B
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SA
li
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se
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C
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r
r
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p
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A
uth
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r
:
Md
.
Haz
r
at
Ali
,
Dep
ar
tm
en
t
o
f
Me
ch
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ical
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d
Aer
o
s
p
ac
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E
n
g
in
ee
r
in
g
,
SEDS,
Naz
ar
b
ay
e
v
Un
iv
er
s
ity
,
5
3
Kab
n
a
b
ay
B
aty
r
Av
e,
0
1
0
0
0
0
Nu
r
-
Su
ltan
,
Kaz
ak
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s
tan
.
E
m
ail: m
d
.
ali@
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.
ed
u
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k
z
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
r
esear
ch
o
n
t
h
e
s
tab
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y
o
f
h
i
g
h
er
-
o
r
d
e
r
s
y
s
tem
s
was
in
itiated
b
y
E
d
war
d
R
o
u
th
an
d
Ad
o
l
f
Hu
r
witz
lo
n
g
ag
o
,
th
eir
th
eo
r
y
is
b
ein
g
u
s
ed
n
o
w
b
y
co
n
tr
o
l
ex
p
er
ts
wh
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an
aly
s
in
g
th
e
s
tab
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o
f
d
y
n
am
ic
s
y
s
tem
s
an
d
ad
d
ed
to
m
an
y
b
o
o
k
s
o
n
co
n
tr
o
l
en
g
in
ee
r
i
n
g
[
1
-
4
]
.
I
t
p
r
o
v
id
es
an
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ec
tiv
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to
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n
d
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ts
o
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ly
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m
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jω
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ax
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s
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p
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Nev
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h
eless
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ically
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atica
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b
ased
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n
t
h
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R
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s
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lu
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
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m
p
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t E
l Co
n
tr
o
l
A
n
o
ve
l tw
o
-
p
o
ly
n
o
mia
l c
r
eteria
fo
r
h
ig
h
er o
r
d
er sys
tems st
a
b
ilit
y
b
o
u
n
s
a
r
ies..
.
(
Md
.
Ha
z
r
a
t A
li
)
3165
So
m
e
r
esear
ch
er
s
h
a
v
e
m
an
ag
ed
to
s
o
lv
e
s
p
ec
if
ic
s
y
s
tem
s
tab
ilit
y
p
r
o
b
lem
s
b
y
u
s
in
g
th
e
R
o
u
th
-
Hu
r
witz
cr
iter
io
n
.
I
n
p
ap
er
[
5
]
,
th
e
au
th
o
r
s
u
s
ed
t
h
e
Her
m
ite
-
B
ieh
ler
th
eo
r
em
to
d
er
iv
e
th
e
R
o
u
th
-
Hu
r
witz
cr
iter
io
n
a
n
d
m
an
ag
e
d
to
ca
p
tu
r
e
th
e
s
y
s
tem
’
s
u
n
s
tab
le
r
o
o
t
co
u
n
tin
g
.
W
h
ile
p
er
f
o
r
m
in
g
s
tab
ilit
y
an
aly
s
is
,
th
e
R
o
u
th
a
r
r
ay
m
ay
s
u
f
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er
s
o
m
e
s
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g
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lar
ities
.
On
e
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am
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le
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en
th
e
f
ir
s
t
elem
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t
o
f
a
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w
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n
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o
u
t
t
o
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e
ze
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o
.
T
h
e
s
o
lu
tio
n
to
t
h
is
ca
s
e
was
d
is
cu
s
s
ed
in
s
o
m
e
p
a
p
er
s
[
5
-
7
]
a
n
d
tex
tb
o
o
k
s
[
1
-
4
]
.
So
m
e
r
esear
ch
er
s
h
av
e
u
s
ed
th
e
ϵ
-
m
eth
o
d
to
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o
lv
e
th
e
s
tab
ilit
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p
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o
b
lem
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o
r
th
e
s
p
ec
ial
ca
s
e
wh
en
th
er
e
ar
e
ze
r
o
lef
tm
o
s
t
elem
en
ts
to
g
eth
er
with
an
all
-
ze
r
o
r
o
w
in
th
e
R
o
u
th
ar
r
ay
[
6
]
.
A
m
in
o
r
r
ec
o
n
s
tr
u
cti
o
n
o
f
R
o
u
th
’
s
a
r
r
ay
is
d
em
o
n
s
tr
ated
in
[
7
]
to
s
o
l
v
e
a
p
ar
ticu
lar
ca
s
e
o
f
lead
in
g
el
e
m
en
ts
in
th
e
ar
r
a
y
b
ec
o
m
in
g
z
er
o
.
I
n
r
ec
o
n
s
tr
u
cted
ar
r
ay
,
l
o
ca
tio
n
s
o
f
a
p
o
ly
n
o
m
i
al
r
o
o
t
a
r
e
d
e
f
in
ed
b
y
m
ea
n
s
o
f
co
n
s
id
er
in
g
f
ir
s
t
-
co
l
u
m
n
s
ig
n
ch
an
g
es,
s
im
ilar
to
R
o
u
th
’
s
m
eth
o
d
,
wh
ich
elim
in
ates th
e
u
s
e
o
f
th
e
ϵ
-
ap
p
r
o
ac
h
.
T
h
e
s
in
g
u
lar
ity
i
n
th
e
R
o
u
t
h
ar
r
ay
w
o
u
ld
o
cc
u
r
i
n
ca
s
e
o
f
all
elem
en
ts
in
a
r
o
w
b
ec
o
m
e
ze
r
o
.
I
n
[
8
]
,
th
e
au
th
o
r
s
h
av
e
p
r
ese
n
ted
a
s
o
lu
tio
n
f
o
r
th
e
r
o
o
ts
o
f
a
p
o
ly
n
o
m
ial
in
th
e
r
ig
h
t
-
h
a
lf
o
f
s
-
p
lan
e
an
d
o
n
th
e
jω
-
ax
is
f
o
r
th
e
ca
s
e
wh
en
a
f
ew
r
o
w
elem
en
ts
in
th
e
R
o
u
th
ar
r
ay
b
ec
o
m
e
ze
r
o
.
T
h
ey
h
a
v
e
u
s
ed
th
e
co
n
tin
u
ed
f
r
ac
tio
n
a
p
p
r
o
ac
h
to
s
o
lv
e
t
h
e
p
r
o
b
lem
.
W
h
en
a
s
y
s
tem
p
ar
am
eter
is
o
f
t
h
e
ϵ
-
o
r
d
er
,
th
e
ad
v
a
n
tag
e
o
f
th
e
ϵ
-
m
eth
o
d
o
f
th
e
R
o
u
th
-
Hu
r
witz
cr
iter
io
n
f
o
r
th
e
ze
r
o
r
o
ws
was
elab
o
r
ated
i
n
[
9
]
.
I
n
[
1
0
]
,
a
u
th
o
r
s
h
av
e
r
ep
lace
d
ze
r
o
r
o
w
co
ef
f
icien
ts
with
th
e
d
er
iv
ativ
e
o
f
th
e
p
o
ly
n
o
m
ial
co
r
r
esp
o
n
d
in
g
t
o
th
e
r
o
w
n
ex
t
to
th
e
ze
r
o
-
r
o
w
to
f
ill
th
e
r
o
w
as
an
ad
d
itio
n
al
p
r
o
ce
d
u
r
e
an
d
d
o
in
g
th
at
th
ey
h
a
v
e
m
an
ag
ed
to
id
e
n
tify
th
e
p
o
ly
n
o
m
ial
r
o
o
ts
lo
ca
ted
s
y
m
m
etr
ically
o
n
th
e
r
ig
h
t a
n
d
lef
t a
n
d
o
n
th
e
jω
-
a
x
is
.
[
7
]
.
I
m
p
o
r
ta
n
tly
,
th
e
R
o
u
th
-
H
u
r
wi
tz
cr
iter
io
n
u
n
a
b
le
to
d
eter
m
i
n
e
th
e
ca
s
e
o
f
in
s
tab
ilit
y
f
o
r
t
h
e
ca
s
e
o
f
m
u
ltip
le
r
o
o
ts
o
n
th
e
jω
-
ax
i
s
o
f
th
e
s
-
p
lan
e
[
2
,
4
,
1
1
]
.
R
o
u
th
ar
r
ay
d
o
es
n
o
t
p
r
o
v
id
e
a
s
o
lu
tio
n
f
o
r
th
e
n
u
m
b
er
o
f
m
u
ltip
le
jω
-
ax
is
r
o
o
ts
u
n
less
s
o
lv
in
g
i
t
with
th
e
au
x
iliar
y
p
o
ly
n
o
m
ial.
Ho
wev
er
,
e
v
en
th
e
ap
p
licatio
n
o
f
a
u
x
iliar
y
p
r
o
ce
d
u
r
e
d
o
es
n
o
t
s
h
o
w
s
ig
n
ch
an
g
e
in
th
e
f
ir
s
t
co
lu
m
n
o
f
R
o
u
th
’
s
ar
r
ay
f
o
r
s
o
m
e
u
n
s
tab
le
s
y
s
tem
s
th
at
h
av
e
r
ep
ea
ted
m
u
ltip
le
r
o
o
ts
o
n
jω
-
ax
is
an
d
n
o
r
o
o
ts
o
f
th
e
s
y
s
tem
p
o
ly
n
o
m
i
als
in
th
e
r
ig
h
t
h
alf
s
-
p
lan
e
[
1
1
]
.
I
n
[
1
0
]
,
th
e
au
th
o
r
s
ar
e
m
an
ag
e
d
to
co
u
n
t
th
e
n
u
m
b
e
r
o
f
r
o
o
ts
o
n
jω
-
ax
is
th
at
ar
e
co
m
p
lex
p
o
l
y
n
o
m
ials
.
T
h
e
a
u
th
o
r
s
in
[
1
2
]
h
a
v
e
in
v
esti
g
a
ted
p
o
s
s
ib
le
r
elatio
n
b
etwe
en
th
e
m
u
ltip
licity
o
f
jω
-
ax
is
p
o
les
a
n
d
th
e
ze
r
o
r
o
w
s
n
u
m
b
e
r
s
in
th
e
R
o
u
th
a
r
r
ay
.
T
h
e
m
ain
o
u
tco
m
e
was
a
p
r
o
o
f
th
at
th
e
e
x
is
ten
ce
o
f
m
u
ltip
le
ze
r
o
r
o
ws
in
th
e
R
o
u
th
a
r
r
ay
is
a
s
o
u
r
ce
o
f
in
s
ta
b
ilit
y
o
f
th
e
s
y
s
tem
d
esp
ite
s
ig
n
ch
a
n
g
e
in
t
h
e
f
ir
s
t
co
lu
m
n
.
I
n
p
ap
er
[
1
3
]
,
au
th
o
r
s
h
av
e
aim
ed
at
th
e
m
o
d
ellin
g
o
f
cy
clic
p
h
y
s
ical
p
h
en
o
m
e
n
o
n
an
d
in
v
esti
g
ated
h
ar
m
o
n
ic
o
s
cillatio
n
s
o
f
s
y
s
tem
s
at
th
e
b
o
r
d
er
s
o
f
s
tab
ilit
y
r
eg
io
n
s
.
Stab
ilit
y
b
o
u
n
d
ar
y
o
s
cillatio
n
s
ar
e
u
s
ed
in
m
an
y
s
cien
ce
an
d
e
n
g
in
ee
r
in
g
ap
p
licatio
n
s
[
1
3
]
.
T
h
e
a
u
th
o
r
s
in
[
1
4
,
1
5
]
c
o
n
d
u
c
ted
b
o
u
n
d
a
r
y
lo
cu
s
an
a
ly
s
is
to
ac
h
iev
e
a
s
tab
le
co
n
tr
o
l sy
s
te
m
d
esig
n
.
T
h
e
au
th
o
r
s
id
en
tifi
ed
s
tab
ilit
y
r
eg
io
n
s
o
f
co
n
tr
o
ll
er
co
ef
f
icien
ts
b
ased
o
n
a
s
o
lu
tio
n
o
f
ch
a
r
ac
ter
is
tic
eq
u
atio
n
in
s
d
o
m
ain
(
s
=
jω
).
I
n
th
e
r
esear
ch
p
ap
er
[
1
3
]
,
th
e
au
th
o
r
s
h
av
e
id
en
t
if
ied
th
e
h
ar
m
o
n
ic
o
s
c
illatio
n
b
o
u
n
d
ar
y
o
f
s
y
s
tem
s
b
y
m
atch
in
g
th
e
r
o
o
ts
o
f
th
e
ch
ar
ac
ter
is
tic
p
o
ly
n
o
m
ial
with
am
p
litu
d
e
-
an
g
le
(
−
)
p
lan
e
a
n
d
r
ep
r
esen
ti
n
g
r
o
o
ts
o
f
th
e
p
o
ly
n
o
m
ial
as λ
=
.
An
o
th
er
co
m
m
o
n
m
et
h
o
d
o
f
n
-
th
o
r
d
er
s
y
s
tem
s
s
tab
ilit
y
s
tu
d
ies
is
r
elate
d
to
an
al
y
s
in
g
n
u
m
er
ical
eig
en
v
alu
es
o
f
n
s
tate
eq
u
atio
n
s
[
1
6
,
1
7
]
.
Ho
wev
er
,
it
d
o
es
n
o
t
s
im
p
lify
th
e
s
o
lu
tio
n
o
f
th
e
p
r
o
b
lem
f
o
r
th
e
n
-
th
o
r
d
e
r
s
y
s
tem
,
th
e
d
im
en
s
io
n
s
o
f
a
m
atr
ix
o
f
eig
en
v
a
lu
es
an
d
m
atr
ix
A
,
i.e
.
(
λ
I
-
A
)
,
ar
e
o
f
th
e
s
am
e
n
-
th
o
r
d
er
.
T
h
er
ef
o
r
e,
t
h
e
lev
el
o
f
co
m
p
lex
ity
o
f
s
tab
ilit
y
p
r
o
b
le
m
s
o
lu
tio
n
is
th
e
s
am
e
as
to
l
o
o
k
in
t
o
th
e
r
o
o
ts
o
f
th
e
o
r
ig
in
al
n
-
th
o
r
d
er
s
y
s
tem
ch
ar
ac
t
er
is
tic
p
o
ly
n
o
m
ial.
I
n
o
th
er
wo
r
d
s
,
it
r
eq
u
ir
es
ca
lc
u
latio
n
n
u
m
er
ically
th
e
r
o
o
ts
λ
o
f
n
-
th
o
r
d
er
p
o
ly
n
o
m
ial
to
v
er
if
y
th
e
s
tab
ilit
y
o
f
a
g
iv
en
s
y
s
tem
.
T
h
er
ef
o
r
e
th
e
an
aly
tical
s
o
lu
tio
n
o
f
th
e
p
r
o
b
lem
is
n
o
t
p
o
s
s
ib
le.
T
h
e
n
ew
t
h
eo
r
y
o
f
s
tab
ilit
y
wa
s
in
iti
ally
in
tr
o
d
u
ce
d
in
[
1
8
]
a
n
d
s
u
cc
ess
f
u
lly
u
s
ed
to
id
en
tify
th
e
b
o
u
n
d
ar
y
co
n
d
itio
n
s
an
aly
tically
f
o
r
u
p
to
s
ix
th
o
r
d
er
s
y
s
tem
s
.
T
h
e
L
a
p
lace
tr
an
s
f
o
r
m
o
f
p
o
ly
n
o
m
ial
eq
u
atio
n
is
in
tr
o
d
u
ce
d
,
an
d
th
e
m
an
i
p
u
latio
n
o
f
s
ig
n
als
an
d
s
y
s
tem
s
in
ter
m
s
o
f
s
tab
ilit
y
in
th
e
L
ap
lace
d
o
m
ai
n
ex
p
lain
ed
[
1
9
]
.
An
o
th
er
wo
r
k
p
r
esen
ts
s
im
p
le
to
o
ls
to
q
u
ick
ly
d
eter
m
i
n
e
wh
eth
er
a
g
iv
en
s
y
s
tem
is
s
tab
le,
an
d
to
d
eter
m
in
e
th
e
v
alu
e
r
an
g
e
o
f
c
o
ef
f
icien
ts
[
2
0
]
.
Glo
b
al
asy
m
p
to
tic
s
tab
ilit
y
o
f
th
e
eq
u
ilib
r
iu
m
p
o
in
t
o
f
a
d
elay
ed
s
y
s
tem
g
i
v
e
n
b
y
a
h
ig
h
e
r
-
o
r
d
e
r
d
ela
y
ed
d
if
f
er
en
tial
e
q
u
atio
n
o
f
r
etar
d
e
d
ty
p
e
with
s
ev
er
al
tim
e
-
v
ar
y
i
n
g
d
ela
y
s
is
ex
ap
lin
e
d
[
2
1
]
.
A
h
ig
h
er
-
o
r
d
er
s
h
ea
r
d
ef
o
r
m
atio
n
th
e
o
r
y
is
u
s
ed
to
d
eter
m
in
e
th
e
s
tab
ilit
y
o
f
elastic
p
lates
in
[
2
2
]
.
Stab
ilit
y
b
o
u
n
d
a
r
ies
an
d
later
a
l
p
o
s
tu
r
e
co
n
tr
o
l
is
d
is
ce
r
ib
ed
in
[
2
3
]
.
T
h
e
liter
atu
r
e
r
ev
iew
h
as
s
h
o
wn
th
at
s
o
f
ar
th
er
e
is
n
o
an
y
s
y
s
tem
atic
an
d
ex
ac
t
s
o
lu
tio
n
f
o
r
s
tab
ilit
y
p
r
o
b
lem
o
f
lin
ea
r
h
ig
h
e
r
-
o
r
d
er
d
y
n
am
ic
s
y
s
tem
s
th
at
ca
n
id
e
n
t
if
y
ex
ac
t
s
tab
ilit
y
b
o
u
n
d
a
r
ies
o
f
s
y
s
tem
b
eh
av
io
u
r
th
r
o
u
g
h
th
e
c
o
ef
f
icien
ts
o
f
its
p
o
ly
n
o
m
ial
e
q
u
atio
n
an
d
d
o
in
g
th
at
is
ab
le
th
o
r
o
u
g
h
l
y
to
a
n
aly
s
e
an
d
d
if
f
e
r
en
tiate
m
ar
g
in
al
s
tab
ilit
y
o
r
i
n
s
tab
ilit
y
o
f
s
y
s
tem
s
at
th
e
b
o
u
n
d
ar
y
r
eg
io
n
s
o
f
s
tab
ilit
y
.
T
h
e
im
p
o
r
t
an
ce
o
f
s
u
c
h
th
eo
r
y
co
u
ld
also
c
o
n
tr
ib
u
te
to
clo
s
ed
-
lo
o
p
co
n
tr
o
ller
s
d
esig
n
an
d
s
elec
tio
n
o
f
g
ain
s
f
o
r
t
h
e
co
n
tr
o
ller
o
f
d
y
n
am
i
c
s
y
s
tem
s
.
T
h
e
clo
s
e
d
-
lo
o
p
co
n
tr
o
ller
g
ain
s
ar
e
p
ar
t
o
f
th
e
s
y
s
tem
ch
ar
ac
ter
is
tic
p
o
ly
n
o
m
i
al
co
ef
f
icien
ts
an
d
,
th
er
ef
o
r
e,
s
tab
ilit
y
lim
its
o
f
th
e
co
ef
f
icien
ts
ca
n
b
e
u
s
ed
,
in
tu
r
n
,
to
id
en
tif
y
s
tab
ilit
y
l
im
its
f
o
r
th
e
g
ain
s
.
T
h
e
m
eth
o
d
d
escr
ib
ed
in
th
is
p
ap
er
aim
s
to
s
o
lv
e
t
h
ese
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r
o
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B
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it
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n
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ely
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n
th
e
s
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ile
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th
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il
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e
s
p
ec
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ca
s
es o
f
ze
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o
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e
f
f
i
cien
ts
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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ith
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ates
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an
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d
esig
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[
2
5
]
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
G
ener
a
l st
a
bil
it
y
cr
it
er
i
a
I
n
g
e
n
e
r
a
l
,
t
h
e
c
h
a
r
a
c
t
e
r
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s
t
i
c
p
o
l
y
n
o
m
i
a
l
f
o
r
t
h
e
h
i
g
h
e
r
-
o
r
d
e
r
d
y
n
a
m
i
c
s
y
s
t
e
m
c
a
n
b
e
p
r
e
s
e
n
t
e
d
a
s
f
o
l
l
o
w
s
:
+
−
1
−
1
+
−
2
−
2
+
⋯
+
1
+
0
=
0
(
1
)
O
n
e
o
f
t
h
e
c
o
n
d
i
t
i
o
n
s
o
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o
s
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ta
b
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it
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s
t
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at
a
l
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t
h
e
c
o
e
f
f
i
c
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e
n
ts
o
f
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h
e
p
o
l
y
n
o
m
i
a
l
m
u
s
t
b
e
p
o
s
i
ti
v
e
r
e
al
n
u
m
b
e
r
s
[
2
3
]
.
H
o
w
e
v
e
r
,
p
o
s
i
ti
v
e
v
a
l
u
e
s
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e
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p
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a
b
il
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t
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o
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y
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e
m
.
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h
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r
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p
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m
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o
m
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o
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f
f
ic
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ts
h
a
v
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s
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w
h
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d
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s
tab
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t
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a
b
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y
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h
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e
r
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t
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a
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e
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a
m
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c
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t
e
m
(
w
h
e
r
e
n
≥
3
)
c
a
n
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e
s
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l
e
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y
e
x
p
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e
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y
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e
t
o
f
t
w
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n
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n
l
i
n
e
a
r
(
2
)
o
r
(
3
)
w
i
t
h
t
h
e
i
n
t
r
o
d
u
c
t
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o
n
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f
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a
d
d
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t
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l
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k
n
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w
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v
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r
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a
b
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t
h
a
t
c
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p
l
es
b
o
t
h
e
q
u
a
t
i
o
n
s
t
o
g
e
t
h
e
r
.
I
f
t
h
e
s
y
s
t
em
o
r
d
e
r
n
i
s
a
n
odd
n
u
m
b
e
r
,
t
h
e
n
t
w
o
e
q
u
a
t
i
o
n
s
a
r
e
p
r
e
s
e
n
te
d
,
a
s
f
o
l
l
o
ws
:
=
(
−
2
−
(
−
4
−
⋯
−
(
3
−
1
)
)
…
)
(
2
)
−
1
=
(
−
3
−
(
−
5
−
⋯
−
(
2
−
0
)
)
…
)
I
f
th
e
h
i
g
h
est
o
r
d
e
r
o
f
th
e
s
y
s
tem
n
is
an
even
n
u
m
b
er
,
t
h
en
t
wo
eq
u
atio
n
s
ar
e
p
r
esen
ted
d
if
f
er
en
tly
,
as
f
o
llo
ws:
=
(
−
2
−
(
−
4
−
⋯
−
(
2
−
0
)
)
…
)
(
3
)
−
1
=
(
−
3
−
(
−
5
−
⋯
−
(
3
−
1
)
)
…
)
I
t
ca
n
b
e
s
ee
n
f
r
o
m
(
2
)
an
d
(
3
)
th
at
u
n
k
n
o
wn
p
ar
a
m
eter
k
m
u
s
t
b
e
a
r
ea
l
p
o
s
itiv
e
n
u
m
b
e
r
to
en
s
u
r
e
th
at
co
ef
f
icien
ts
an
d
−
1
ar
e
p
o
s
itiv
e
r
ea
l
n
u
m
b
er
s
,
wh
ich
is
an
o
b
v
io
u
s
s
tab
ilit
y
co
n
d
itio
n
f
o
r
th
e
s
y
s
tem
.
T
h
e
f
u
n
d
am
e
n
tal
law
o
f
m
ar
g
in
al
o
r
b
o
u
n
d
a
r
y
s
tab
ilit
y
o
f
a
n
y
d
y
n
am
ic
s
y
s
tem
with
o
r
d
e
r
≥
3
is
s
tated
as
f
o
llo
ws:
“if
(
2
)
o
r
(
3
)
a
r
e
s
atis
f
ied
an
d
th
er
e
e
x
is
ts
a
s
o
lu
tio
n
o
f
th
ese
eq
u
a
tio
n
s
with
at
leas
t o
n
e
co
m
m
o
n
k
as
a
p
o
s
itiv
e
r
ea
l
r
o
o
t,
th
en
all
th
e
co
ef
f
icien
ts
in
(
1
)
ar
e
h
a
v
in
g
s
tab
ilit
y
b
o
u
n
d
a
r
y
v
alu
es
an
d
th
e
s
y
s
tem
u
n
d
er
co
n
s
id
er
atio
n
is
in
th
e
s
tate
o
f
m
ar
g
in
al
o
r
b
o
u
n
d
ar
y
s
tab
ilit
y
co
n
d
itio
n
”.
At
th
is
s
ta
g
e
,
s
o
m
e
o
f
th
e
r
o
o
t
s
o
f
ch
ar
ac
ter
is
tic
p
o
ly
n
o
m
ial
(
1
)
f
o
r
m
co
n
j
u
g
ate
p
air
s
an
d
s
tr
ictly
lo
ca
ted
o
n
th
e
im
a
g
in
ar
y
jω
-
ax
is
o
f
th
e
s
-
p
lan
e.
T
h
er
ef
o
r
e,
(
2
)
o
r
(
3
)
r
ep
r
esen
t
th
e
n
ec
ess
ar
y
an
d
s
u
f
f
icien
t
cr
i
ter
ia
to
d
ef
in
e
ac
c
u
r
ately
s
tab
il
ity
b
o
u
n
d
ar
y
v
alu
e
f
o
r
all
th
e
c
o
ef
f
icien
t
o
f
s
y
s
tem
s
with
ch
ar
ac
ter
is
tic
p
o
ly
n
o
m
ial
o
r
d
er
≥
3
,
p
r
o
v
id
e
d
alg
eb
r
a
ic
(
2
)
,
o
r
(
3
)
h
a
v
e
at
least
o
n
e
co
m
m
o
n
p
o
s
itiv
e
r
ea
l
s
o
lu
tio
n
f
o
r
k
.
I
n
o
t
h
er
wo
r
d
s
,
if
c
o
n
d
itio
n
s
(
2
)
o
r
(
3
)
s
atis
f
y
,
t
h
en
th
e
d
y
n
a
m
ic
s
y
s
tem
is
in
th
e
s
tate
o
f
m
ar
g
in
al
s
tab
ilit
y
o
r
in
s
tab
ilit
y
,
i.e
.
,
it
is
p
r
ec
is
e
ly
in
b
etwe
en
th
e
s
tab
le
an
d
u
n
s
tab
le
zo
n
es
o
f
b
e
h
av
io
u
r
.
T
h
e
b
o
u
n
d
ar
y
v
al
u
es
f
o
r
th
e
co
ef
f
icie
n
ts
o
f
th
e
n
-
t
h
o
r
d
er
s
y
s
tem
(
1
)
ca
n
b
e
o
b
tain
ed
b
y
m
ath
em
atica
lly
ex
clu
d
in
g
u
n
k
n
o
wn
k
f
r
o
m
b
o
th
(
2
)
o
r
(
3
)
.
T
h
e
n
ewly
d
ev
el
o
p
ed
(
2
)
o
r
(
3
)
h
av
e
n
o
a
n
alo
g
y
to
an
y
s
tab
ilit
y
cr
iter
ia
s
h
o
wn
s
o
f
ar
in
th
e
liter
atu
r
e.
T
h
e
r
ela
tio
n
s
h
ip
b
etwe
en
th
e
co
ef
f
icien
ts
o
f
th
e
ch
ar
ac
ter
is
tic
p
o
ly
n
o
m
ial
at
th
e
s
tate
o
f
s
y
s
tem
s
tab
ilit
y
b
o
u
n
d
ar
y
r
eg
io
n
s
h
as
b
ee
n
d
is
co
v
er
e
d
in
tu
itiv
ely
.
Sti
ll,
i
t
ca
n
b
e
v
er
if
ied
b
y
an
y
o
th
er
m
eth
o
d
t
h
at
d
escr
ib
es st
ab
ilit
y
b
o
u
n
d
ar
y
co
n
d
itio
n
s
f
o
r
a
d
y
n
am
ic
s
y
s
tem
.
3.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
3
.
1
.
S
t
a
bil
it
y
ra
ng
e
f
o
r
t
he
c
lo
s
ed
-
lo
o
p c
o
ntr
o
l sy
s
t
em
s
I
n
(
4
)
,
R
(
s
)
is
th
e
in
p
u
t
s
ig
n
al,
Y(s)
is
th
e
o
u
tp
u
t
s
ig
n
al,
H(
s
)
is
th
e
f
ee
d
b
ac
k
s
ig
n
al,
G(
s
)
is
th
e
p
lan
t
m
o
d
el
(
s
y
s
tem
u
n
d
er
o
b
s
er
v
atio
n
)
,
an
d
K
(
s
)
is
th
e
co
n
tr
o
lle
r
m
o
d
el.
I
n
(
2
)
o
r
(
3
)
ca
n
b
e
s
u
c
ce
s
s
f
u
lly
ap
p
lied
to
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
A
n
o
ve
l tw
o
-
p
o
ly
n
o
mia
l c
r
eteria
fo
r
h
ig
h
er o
r
d
er sys
tems st
a
b
ilit
y
b
o
u
n
s
a
r
ies..
.
(
Md
.
Ha
z
r
a
t A
li
)
3167
id
en
tify
s
tab
ilit
y
r
an
g
es
f
o
r
th
e
g
ain
s
o
f
t
h
e
clo
s
ed
-
l
o
o
p
co
n
tr
o
l sy
s
tem
(
4
)
.
T
h
e
s
-
d
o
m
ain
t
r
an
s
f
er
f
u
n
ctio
n
f
o
r
th
e
clo
s
ed
-
lo
o
p
co
n
tr
o
l sy
s
tem
ca
n
b
e
e
x
p
r
ess
ed
as f
o
llo
ws:
(
)
(
)
=
(
)
(
)
1
+
(
)
(
)
(
)
(
4
)
3
.
1
.
1
.
Ca
s
e
o
f
s
ing
le
g
a
in co
n
t
ro
ller
des
ig
n
T
h
e
s
tab
ilit
y
an
aly
s
is
o
f
a
s
y
s
t
em
with
a
s
in
g
le
g
ain
co
n
tr
o
ll
er
ca
n
b
e
d
em
o
n
s
tr
ated
o
n
th
e
m
o
d
el
o
f
a
h
ar
d
d
is
k
d
r
iv
e
with
th
e
lead
co
m
p
en
s
ato
r
.
T
h
e
p
lan
t
m
o
d
el
o
f
th
e
h
ar
d
d
is
k
d
r
iv
e
s
y
s
tem
ca
n
b
e
ex
p
r
ess
ed
as f
o
llo
ws [
1
9
]
:
(
)
=
/
(
5
)
=
4
4
+
3
3
+
2
2
+
1
+
0
,
=
10
10
+
9
9
+
8
8
+
∙
∙
∙
+
4
4
+
3
3
+
2
2
,
wh
er
e:
4
=
1
.
197
∙
10
26
,
3
=
2
.
12
∙
10
29
,
2
=
5
.
826
∙
10
34
,
1
=
4
.
366
∙
10
37
,
0
=
6
.
189
∙
10
42
,
10
=
1
,
9
=
5336
,
8
=
4
.
124
∙
10
9
,
7
=
1
.
302
∙
10
13
,
6
=
4
.
216
∙
10
18
,
5
=
6
.
72
∙
10
21
,
4
=
1
.
198
∙
10
27
,
3
=
7
.
496
∙
10
29
,
2
=
9
.
668
∙
10
34
.
T
h
e
lead
co
m
p
en
s
ato
r
with
a
p
r
o
p
o
r
tio
n
al
g
ain
k
p
ca
n
b
e
p
r
esen
ted
as f
o
llo
ws:
(
)
=
(
4
+
2
)
/
(
+
2
)
(
6
)
Su
b
s
titu
tin
g
(
5
)
,
(
6
)
in
to
(
4
)
an
d
ass
u
m
in
g
(
)
=
1
,
y
ield
s
th
e
f
o
llo
win
g
clo
s
e
-
lo
o
p
s
y
s
tem
ch
ar
ac
ter
is
tic
p
o
ly
n
o
m
ial
o
f
1
1
th
or
d
er
d
y
n
a
m
ic
s
y
s
tem
,
wh
er
e:
11
=
10
,
10
=
9
+
2
10
,
9
=
8
+
2
9
,
8
=
7
+
2
8
,
7
=
6
+
12
7
,
6
=
5
+
2
6
,
5
=
4
+
2
5
+
4
4
,
4
=
3
+
2
4
+
2
(
2
3
+
4
)
,
3
=
2
+
2
3
+
2
(
2
2
+
3
)
,
2
=
2
2
+
2
(
2
1
+
2
)
,
1
=
2
(
2
0
+
1
)
,
0
=
2
0
.
Fo
r
th
e
elev
en
th
(
o
d
d
)
o
r
d
er
c
h
ar
ac
ter
is
tic
p
o
ly
n
o
m
ial,
two
s
tab
ilit
y
b
o
u
n
d
ar
y
p
o
ly
n
o
m
ial
s
ca
n
b
e
p
r
esen
ted
as
(
2
)
.
B
y
s
u
b
s
titu
tin
g
all
th
e
c
o
ef
f
icien
ts
in
to
(
2
)
an
d
d
iv
id
in
g
o
n
e
b
y
an
o
th
er
,
th
e
p
r
o
p
o
r
ti
o
n
al
g
ain
ca
n
b
e
ex
clu
d
ed
f
r
o
m
th
e
r
esu
ltin
g
s
i
n
g
le
alg
eb
r
aic
6
th
o
r
d
er
s
tab
ilit
y
b
o
u
n
d
ar
y
eq
u
atio
n
with
v
a
r
i
ab
le
k
as f
o
llo
ws:
6
6
+
5
5
+
4
4
+
3
3
+
2
2
+
1
+
0
,
(
7
)
w
h
er
e
co
ef
f
icien
ts
ar
e
f
u
n
ctio
n
s
o
f
o
n
l
y
g
iv
e
n
co
n
s
tan
t
p
ar
a
m
eter
s
.
T
h
e
s
o
lu
tio
n
o
f
(
7
)
y
ield
s
f
o
u
r
r
ea
l
an
d
two
co
m
p
lex
k
r
o
o
t
s
.
I
n
ac
co
r
d
an
ce
with
r
u
les
o
f
s
tab
ilit
y
,
o
n
ly
r
ea
l
r
o
o
ts
o
f
(
7
)
co
u
ld
b
e
co
n
s
id
er
ed
f
o
r
th
e
m
ar
g
in
al
s
tab
ilit
y
o
f
t
h
e
clo
s
ed
-
l
o
o
p
s
y
s
tem
.
Fo
u
r
r
ea
l
r
o
o
ts
ar
e
0
.
4
9
1
2
*
1
0
-
6
,
0
.
0
1
3
9
*
1
0
-
6
,
0
.
0
0
7
7
*
1
0
-
6
,
0
.
0
0
0
6
*
1
0
-
6
.
Va
lu
e
o
f
at
th
e
s
tate
o
f
m
ar
g
in
al
s
tab
ilit
y
ca
n
b
e
ca
lcu
lated
f
r
o
m
(
3
2
)
an
d
p
r
ese
n
ted
as f
o
llo
ws:
=
C
/D,
wh
er
e
(
8
)
C
=
11
−
9
+
7
2
−
5
3
+
3
4
−
1
5
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
6
,
Dec
em
b
e
r
2
0
2
0
:
316
4
-
317
2
3168
D
=
5
3
−
3
4
+
1
5
.
Su
b
s
titu
tin
g
f
o
u
r
r
ea
l
r
o
o
ts
o
f
(
7
)
in
to
(
8
)
y
ield
th
r
ee
p
o
s
itiv
es
an
d
o
n
e
n
eg
ativ
e
v
alu
es
o
f
.
Neg
ativ
e
v
alu
e
lead
s
to
in
s
tab
ilit
y
o
f
th
e
s
y
s
tem
b
ec
au
s
e
o
f
t
h
e
co
ef
f
icien
t
0
o
f
th
e
s
y
s
tem
is
d
ir
ec
tly
p
r
o
p
o
r
tio
n
al
to
,
i.e
.
0
=
2
0
,
an
d
ca
n
n
o
t b
e
n
eg
ativ
e.
As a
r
esu
lt,
th
e
m
in
im
u
m
s
tab
ilit
y
l
im
it f
o
r
th
e
is
ze
r
o
,
i.
e.
=
0
.
T
h
e
r
em
ain
i
n
g
t
h
r
ee
ca
lcu
lated
p
o
s
itiv
e
v
alu
e
f
o
r
ar
e
0
.
0
0
7
9
,
0
.
2
1
1
9
,
0
.
1
7
2
6
.
So
lv
in
g
f
o
r
th
e
r
o
o
ts
o
f
elev
e
n
th
o
r
d
er
ch
a
r
ac
ter
is
tic
p
o
ly
n
o
m
ial
f
o
r
th
es
e
th
r
ee
v
alu
es
o
f
y
ield
s
a
p
air
o
f
r
o
o
ts
lo
ca
ted
o
n
th
e
im
ag
in
ar
y
ax
i
s
o
f
s
-
p
lan
e
±
0
.
1427
∗
10
4
,
±
0
.
8488
∗
10
4
,
±
1
.
1411
∗
10
4
,
r
esp
ec
tiv
ely
.
T
h
e
an
aly
s
is
o
f
all
s
o
lu
tio
n
s
s
h
o
ws
th
at
o
n
l
y
o
n
e
g
ain
v
alu
e
=0
.
0
0
7
9
co
r
r
esp
o
n
d
s
to
th
e
m
ar
g
in
al
s
tab
ilit
y
co
n
d
itio
n
o
f
th
e
clo
s
ed
-
l
o
o
p
s
y
s
tem
,
wh
er
e
all
th
e
r
o
o
ts
lo
ca
ted
at
th
e
lef
t h
alf
o
f
t
h
e
s
-
p
lan
e.
3.
1
.
2
.
Ca
s
e
o
f
m
ultiple g
a
in co
ntr
o
ller
des
ig
n
T
h
e
ad
v
an
tag
e
o
f
ap
p
ly
i
n
g
(
2
)
an
d
(
3
)
f
o
r
s
tab
ilit
y
an
aly
s
is
o
f
h
ig
h
e
r
-
o
r
d
er
cl
o
s
ed
-
lo
o
p
d
y
n
am
ic
s
y
s
tem
s
ca
n
b
e
d
em
o
n
s
tr
ated
f
o
r
th
e
ca
s
e
o
f
ap
p
ly
in
g
m
u
ltip
le
g
ain
co
n
tr
o
ller
s
to
th
e
s
y
s
tem
.
T
h
e
cr
iter
ia
(
2
)
an
d
(
3
)
w
er
e
test
ed
o
n
th
e
ex
a
m
p
le
o
f
th
e
m
o
d
el
o
f
a
two
-
i
n
er
tia
s
y
s
tem
with
a
p
r
o
p
o
r
tio
n
al
-
d
if
f
er
en
tial
(
PD
)
co
n
tr
o
ller
.
T
h
e
p
lan
t
m
o
d
el
o
f
s
u
ch
a
two
-
in
er
tia
s
y
s
tem
ca
n
b
e
ex
p
r
ess
ed
as f
o
llo
ws [
2
0
]
:
(
)
=
0
/
(
4
4
+
3
3
+
2
2
+
1
+
0
)
,
wh
er
e:
(
9
)
0
=
0
.
0625
,
4
=
1
,
3
=
2
,
2
=
1
.
5
,
1
=
0
.
5
,
0
=
0
.
0625
.
Su
b
s
titu
tin
g
(
9
)
,
(
)
=
+
in
to
(
4
)
an
d
ass
u
m
in
g
(
)
=
1
y
ield
s
th
e
f
o
llo
win
g
f
o
u
r
th
-
o
r
d
e
r
ch
ar
ac
ter
is
tic
p
o
ly
n
o
m
ial
o
f
th
e
clo
s
ed
-
lo
o
p
s
y
s
tem
:
4
4
+
3
3
+
2
2
+
(
1
+
0
)
+
(
0
+
0
)
=
0
(
1
0
)
T
h
e
t
w
o
s
t
a
b
i
l
i
t
y
b
o
u
n
d
a
r
y
p
o
l
y
n
o
m
i
a
l
s
(
3
)
f
o
r
t
h
e
c
h
a
r
a
c
t
e
r
i
s
t
i
c
p
o
l
y
n
o
m
i
a
l
(
1
0
.
4
5
)
c
a
n
b
e
p
r
e
s
e
n
t
e
d
a
s
f
o
l
l
o
w
s
:
4
=
2
−
2
(
0
+
0
)
(
1
1
)
3
=
(
1
+
0
)
(
1
2
)
B
y
d
iv
id
in
g
(
1
1
)
b
y
(
1
2
)
,
th
e
f
o
llo
win
g
ex
p
r
ess
io
n
f
o
r
ca
n
b
e
d
er
iv
ed
:
=
[
2
3
−
3
(
0
−
0
)
−
1
4
]
0
4
⁄
(
1
3
)
Su
b
s
titu
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3
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to
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ield
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e
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ad
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atic
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0
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3
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4
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ted
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llo
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=
[
2
±
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2
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4
4
(
0
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]
2
(
0
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0
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(
1
5
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T
h
e
s
tab
ilit
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o
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n
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ar
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is
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h
iev
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en
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er
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h
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m
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tain
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icien
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ch
ar
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ly
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ial
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u
s
t
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e
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o
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itiv
e.
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h
er
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o
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th
e
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t
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+
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u
s
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r
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n
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e
ca
lcu
lated
as f
o
llo
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=
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0
(
1
7
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T
o
p
r
o
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id
e
a
b
s
o
lu
te
s
tab
ilit
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o
f
th
e
clo
s
ed
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o
p
s
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tem
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e
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llo
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n
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itio
n
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o
r
m
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t b
e
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r
o
v
i
d
ed
:
Evaluation Warning : The document was created with Spire.PDF for Python.
T
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L
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o
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p
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3169
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r
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n
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ilit
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n
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itio
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(
1
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,
(
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(
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g
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ap
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u
r
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r
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ials
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5
5
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n
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e
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=
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,
(
21)
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(
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2
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y
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4
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Su
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g
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3
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ield
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atic
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:
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4
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e
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(
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4
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n
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e
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ted
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o
llo
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(
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h
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s
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n
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d
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ield
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a
s
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r
(
s
ta
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).
T
h
is
co
n
d
itio
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ie
ld
s
th
e
f
o
llo
wi
n
g
b
o
u
n
d
ar
y
e
q
u
atio
n
f
o
r
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
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T
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ied
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f
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ield
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RE
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NC
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S
[1
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N.
S
.
Nise
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“
Tran
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[2
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R.
C.
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[3
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M
.
G
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“
Co
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Ru
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4
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.
[4
]
B.
Ku
o
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n
d
M
.
F
.
G
o
ln
a
ra
g
h
i,
“
S
t
a
b
il
it
y
o
f
li
n
e
a
r
c
o
n
tr
o
l
sy
ste
m
s,”
in
Au
to
ma
ti
c
Co
n
tr
o
l
S
y
ste
ms
,
7
th
e
d
.
En
g
lew
o
o
d
Cli
ffs,
NJ
:
P
re
n
t
ice
-
Ha
ll
,
c
h
a
p
ter
6
,
se
c
.
5
,
p
p
.
3
3
4
–
3
4
3
,
1
9
9
5
.
[5
]
M
.
Ho
,
A.
Da
tt
a
,
a
n
d
S
.
P
.
Bh
a
tt
a
c
h
a
ry
y
a
,
“
An
e
lem
e
n
tary
d
e
ri
v
a
ti
o
n
o
f
th
e
Ro
u
th
-
H
u
rwitz
c
rit
e
rio
n
,
”
IEE
E
T
ra
n
s.
Au
to
m.
Co
n
tro
l
,
v
o
l.
4
3
,
n
o
.
3
,
p
p
.
4
0
5
-
4
0
9
,
M
a
r
ch
1
9
9
8
.
[6
]
M. M.
Fa
hm
y a
nd
J
. O
’
R
e
il
ly
, “
A
no
te
o
n the
R
o
uth
-
H
u
rwitz t
e
st,”
IEE
E
T
ra
n
s.
Au
t
o
m.
Co
n
tro
l
,
v
o
l.
AC
-
2
7
,
n
o
.
2
,
p
p
.
4
8
3
-
4
8
5
,
Ap
r
il
1
9
8
2
.
[7
]
K.
S
.
Ye
u
n
g
,
“
Ro
u
t
h
-
Hu
rwitz
tes
t
u
n
d
e
r
v
a
n
is
h
in
g
lea
d
in
g
a
rra
y
e
lem
e
n
ts,”
IEE
E
T
ra
n
s.
A
u
to
m.
Co
n
tro
l
,
v
o
l.
AC
-
2
8
,
n
o
.
1
,
p
p
.
1
0
4
-
1
0
6
,
J
a
n
u
a
ry
1
9
8
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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8
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K
.
K
h
a
t
w
a
n
i
,
“
O
n
R
o
u
t
h
-
H
u
r
w
i
t
z
c
r
i
t
e
r
i
o
n
,
”
I
E
E
E
T
r
a
n
s
a
c
t
i
o
n
s
o
n
A
u
t
o
m
a
t
i
c
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n
t
r
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l
,
v
o
l
.
2
6
,
n
o
.
2
,
p
p
.
5
8
3
-
584,
1981.
[9
]
S
.
P
il
lai,
“
Th
e
ε
m
e
th
o
d
o
f
t
h
e
Ro
u
t
h
-
Hu
rwitz
c
rit
e
rio
n
,
”
IEE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
Au
t
o
ma
t
ic
Co
n
tr
o
l
,
v
o
l.
2
6
,
n
o
.
2
,
p
p
.
5
8
4
-
5
8
4
,
Ap
r
il
1
9
8
1
.
[1
0
]
S
.
S
.
Ch
e
n
a
n
d
J.
S
.
H.
Tsa
i,
“
On
t
h
e
sin
g
u
lar
c
a
se
s
o
f
th
e
c
o
m
p
lex
Ro
u
t
h
a
lg
o
rit
h
m
fo
r
sta
b
il
i
ty
tes
ts,”
IM
A
J
.
M
a
t
h
.
Co
n
tr.
I
n
f
o
rm
.
,
v
o
l.
1
0
,
p
p
.
7
1
–
8
2
,
M
a
rc
h
1
9
9
3
.
[
1
1
]
R
.
N
.
C
l
a
r
k
,
“
T
h
e
R
o
u
t
h
-
H
u
r
w
i
t
z
s
t
a
b
i
l
i
t
y
c
r
i
t
e
r
i
o
n
,
r
e
v
i
s
i
t
e
d
,
”
I
E
E
E
C
o
n
t
r
o
l
S
y
s
t
e
m
s
,
v
o
l
.
1
2
,
n
o
.
3
,
p
p
.
1
1
9
-
120,
1992.
[1
2
]
M
.
A.
Ch
o
g
h
a
d
i
a
n
d
H.
A.
Tale
b
i,
“
Th
e
r
o
u
th
-
h
u
rwitz
sta
b
il
it
y
c
rit
e
rio
n
,
re
v
isit
e
d
:
th
e
c
a
se
o
f
m
u
lt
ip
le
p
o
les
o
n
ima
g
in
a
ry
a
x
is
”,
IE
EE
T
r
a
n
sa
c
ti
o
n
s
o
n
A
u
t
o
ma
ti
c
C
o
n
t
r
o
l
,
v
o
l
.
5
8
,
n
o
.
7
,
p
p
.
1
8
6
6
-
1
8
6
9
,
Ju
l
y
2
0
1
3
.
[1
3
]
B.
B.
Ala
g
o
z
,
“
On
t
h
e
h
a
rm
o
n
ic
o
sc
il
latio
n
o
f
h
i
g
h
-
o
rd
e
r
li
n
e
a
r
ti
m
e
-
in
v
a
rian
t
s
y
ste
m
s
”
,
Co
mp
u
ter
S
c
ien
c
e
,
Disc
re
te
M
a
t
h
e
ma
ti
c
s,
a
rXiv
,
p
p
.
1
-
1
2
,
2
0
1
4
.
[1
4
]
N.
Tan
,
“
Co
m
p
u
tatio
n
o
f
S
tab
il
i
z
in
g
P
I
a
n
d
P
ID
c
o
n
tro
ll
e
rs
fo
r
p
ro
c
e
ss
e
s
with
t
ime
d
e
lay
”
,
IS
A
T
ra
n
sa
c
ti
o
n
s
,
v
o
l.
4
4
,
n
o
.
2
,
p
p
2
1
3
-
2
2
3
,
A
p
ril
2
0
0
5
.
[1
5
]
T.
V.
M
o
g
h
a
d
d
a
m
a
n
d
Ab
b
a
si
Y.
“
Tu
n
in
g
a
fra
c
ti
o
n
a
l
o
r
d
e
r
P
D
a
n
d
P
ID
c
o
n
tr
o
ll
e
r
with
lea
d
c
o
m
p
e
n
sa
to
r
f
o
r
i
n
teg
ra
ti
n
g
t
ime
-
d
e
lay
sy
ste
m
s
”
,
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
n
tr
o
l
En
g
i
n
e
e
rin
g
,
v
o
l.
2
,
p
p
3
4
-
4
1
,
2
0
1
4
.
[1
6
]
J.
Ch
e
n
,
P
.
F
u
,
“
S
ta
b
il
it
y
a
n
a
l
y
sis
o
f
p
o
l
y
n
o
m
ially
d
e
p
e
n
d
e
n
t
sy
ste
m
s
b
y
e
ig
e
n
v
a
lu
e
p
e
rtu
r
b
a
ti
o
n
”
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Au
to
ma
ti
c
Co
n
tr
o
l
,
v
o
l
.
6
2
,
iss
u
e
1
1
,
p
p
.
5
9
1
5
-
5
9
2
2
,
2
0
1
7
.
[1
7
]
L.
Wan
g
,
B.
K.
P
.
Ho
r
n
,
G
.
S
tran
g
,
“
Ei
g
e
n
v
a
l
u
e
a
n
d
e
ig
e
n
v
e
c
to
r
a
n
a
ly
sis o
f
sta
b
il
it
y
fo
r
a
li
n
e
o
f
tra
ffic
”
,
S
tu
d
ies
in
Ap
p
li
e
d
M
a
t
h
e
ma
ti
c
s J
o
u
r
n
a
l
,
v
o
l.
1
3
8
,
n
o
.
1
,
p
p
.
1
0
3
-
1
3
2
,
S
e
p
tem
b
e
r
2
0
1
6
.
[1
8
]
N.
M
ir
-
Na
siri,
M
.
H.
Ali
,
“
A
n
e
w
a
lg
o
rit
h
m
to
c
o
n
tr
o
l
d
y
n
a
m
ic
sta
b
il
it
y
o
f
h
i
g
h
e
r
-
o
r
d
e
r
sy
ste
m
s
”
,
Pro
c
e
e
d
in
g
s
o
f
IEE
E
In
ter
n
a
ti
o
n
a
l
C
o
n
fer
e
n
c
e
o
n
Co
n
tro
l
S
y
ste
ms
,
Co
mp
u
ti
n
g
a
n
d
En
g
i
n
e
e
rin
g
,
N
o
v
e
m
b
e
r
2
0
1
8
.
[1
9
]
M
a
rk
A.
Ha
id
e
k
k
e
r,
“
S
o
lv
in
g
Di
ffe
re
n
ti
a
l
Eq
u
a
ti
o
n
s
in
th
e
La
p
lac
e
Do
m
a
in
,
Li
n
e
a
r
F
e
e
d
b
a
c
k
C
o
n
t
ro
ls,
”
El
se
v
ier
,
p
p
.
2
7
-
5
6
,
2
0
1
3
.
[2
0
]
M
a
rk
A.
Ha
id
e
k
k
e
r,
“
S
tab
i
li
ty
A
n
a
ly
sis
fo
r
Li
n
e
a
r
S
y
ste
m
s,
Li
n
e
a
r
F
e
e
d
b
a
c
k
Co
n
tro
ls,
”
El
se
v
ier
,
p
p
.
1
3
9
-
1
4
8
,
2
0
1
3
.
[2
1
]
T
a
k
a
sh
i
A
m
e
m
iy
a
,
“
De
lay
-
in
d
e
p
e
n
d
e
n
t
sta
b
il
it
y
o
f
h
ig
h
e
r
-
o
rd
e
r
s
y
ste
m
s
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Co
n
tro
l
,
v
o
l
.
50
,
n
o
.
1,
p
p
.
1
3
9
-
1
4
9
,
1
9
8
9
.
[2
2
]
J.
N.
Re
d
d
y
,
N.
D.
P
h
a
n
,
“
S
ta
b
il
it
y
a
n
d
v
i
b
ra
ti
o
n
o
f
iso
tr
o
p
ic,
o
rth
o
tro
p
ic
a
n
d
lam
in
a
ted
p
late
s
a
c
c
o
rd
in
g
t
o
a
h
ig
h
e
r
-
o
rd
e
r
sh
e
a
r
d
e
f
o
rm
a
ti
o
n
t
h
e
o
ry
,
”
J
o
u
rn
a
l
o
f
S
o
u
n
d
a
n
d
Vi
b
ra
ti
o
n
,
v
o
l.
9
8
,
n
o
.
2,
p
p
.
1
5
7
-
1
7
0
,
Ja
n
u
a
ry
1
9
8
5
.
[2
3
]
Erwin
E
.
H
.,
et
al
.
,
“
S
tab
il
it
y
b
o
u
n
d
a
ries
a
n
d
late
ra
l
p
o
st
u
re
c
o
n
tro
l
in
p
a
rk
i
n
so
n
d
ise
a
se
,
M
o
t
o
r
c
o
n
tr
o
l
,
v
o
l.
5
,
n
o
.
3
,
p
p
.
2
5
4
-
2
6
9
,
Au
g
u
st
2
0
0
1
.
[2
4
]
A.
Na
th
,
S
.
Ka
it
wa
n
id
v
il
a
i,
“
Hig
h
-
p
e
rfo
rm
a
n
c
e
HD
D
se
rv
o
sy
ste
m
u
sin
g
G
A
b
a
se
d
fix
e
d
st
ru
c
tu
re
ro
b
u
st
lo
o
p
S
h
a
p
i
n
g
c
o
n
tro
l
,
”
Pr
o
c
e
e
d
in
g
s
o
f
IEE
E
In
ter
n
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
R
o
b
o
ti
c
s
a
n
d
Bi
o
mim
e
ti
c
s
(ROB
IO)
,
p
p
.
1
8
5
4
-
1
8
5
9
,
Ja
n
u
a
ry
20
10
.
[2
5
]
G
.
Zh
a
n
g
,
J.
F
u
r
u
sh
o
,
“
S
p
e
e
d
c
o
n
tro
l
o
f
tw
o
-
in
e
rt
ia
sy
ste
m
b
y
P
I
/P
ID
c
o
n
tr
o
l”,
IE
EE
T
r
a
n
sa
c
ti
o
n
s
o
n
I
n
d
u
stria
l
El
e
c
tro
n
ics
,
v
o
l.
4
7
,
no
3
,
p
p
.
6
0
3
-
6
0
9
,
Ju
l
y
2
0
0
0
.
B
I
O
G
RAP
H
I
E
S
O
F
AU
T
H
O
RS
Na
z
im
M
ir
-
Na
sir
i,
fr
o
m
2
0
1
3
u
n
ti
l
2
0
1
9
h
a
d
h
e
ld
t
h
e
p
o
siti
o
n
o
f
P
ro
fe
ss
o
r
o
f
E
lec
tri
c
a
l
a
n
d
El
e
c
tro
n
ics
De
p
a
rtme
n
t
a
t
th
e
S
c
h
o
o
l
o
f
E
n
g
i
n
e
e
rin
g
o
f
Na
z
a
rb
a
y
e
v
Un
i
v
e
rsity
i
n
As
tan
a
,
Ka
z
a
k
h
sta
n
.
Th
r
o
u
g
h
o
u
t
h
is
c
a
r
e
e
r,
h
e
h
a
s
p
u
b
li
s
h
e
d
m
o
re
t
h
a
n
8
0
s
c
ien
ti
fic
p
a
p
e
rs
in
th
e
fiel
d
s o
f
h
is i
n
tere
st:
De
sig
n
o
f
M
e
c
h
a
n
ism
s,
Ro
b
o
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