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1.
I
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UCT
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N
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s
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ated
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m
s
d
u
r
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n
g
t
h
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last
t
w
o
d
ec
ad
es
[
1
-
6
]
.
T
h
e
c
o
n
tr
o
l
p
r
o
b
lem
o
f
co
n
s
tr
ain
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s
.
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th
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ir
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e,
t
h
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o
u
tp
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t
i
s
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tech
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m
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ted
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e
s
y
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te
m
m
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s
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tial
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tatic
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e
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o
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itatio
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.
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n
th
e
s
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o
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d
ca
s
e,
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h
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o
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tp
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t
is
j
u
s
t
an
a
l
y
t
icall
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m
ited
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u
t
tech
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lo
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ll
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n
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ain
t
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n
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n
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ics ca
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o
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t b
e
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.
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n
th
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s
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ap
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d
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s
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r
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n
th
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s
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it
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atio
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t
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ai
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ca
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a
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atin
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eg
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to
s
tab
ilize
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atin
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T
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.
T
h
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n
d
q
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tio
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is
m
o
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t
i
m
p
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tan
t
w
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s
:
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ed
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p
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A
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ilar
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ch
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ties
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h
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s
tab
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o
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g
s
y
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t
e
m
s
w
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f
o
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m
u
lated
b
y
[
7
]
an
d
esp
ec
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all
y
b
y
[
8
]
u
s
in
g
li
n
ea
r
co
n
s
t
r
ain
ed
r
eg
u
lato
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s
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u
t
i
n
th
e
n
o
n
-
d
ela
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ed
s
y
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te
m
s
ca
s
e.
T
h
e
class
o
f
s
y
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te
m
s
co
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s
id
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ed
in
th
e
p
r
esen
t
p
ap
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a
n
d
th
e
o
n
e
in
[
7
]
an
d
[
8
]
d
if
f
e
r
in
th
e
f
ac
t
t
h
at
w
e
ar
e
in
ter
ested
in
s
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s
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d
elay
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in
p
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ain
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en
ter
s
t
h
e
s
y
s
te
m
m
o
d
el.
I
n
[
8
]
an
d
[
7
]
,
th
e
a
u
t
h
o
r
s
s
u
p
p
o
s
ed
th
at
t
h
e
s
tates
ar
e
a
ll
a
v
ailab
le
w
h
ic
h
allo
w
s
u
s
i
n
g
s
tate
-
f
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d
b
ac
k
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e
g
u
la
to
r
,
b
u
t
i
n
o
u
r
p
ap
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w
e
co
n
s
id
er
an
o
u
tp
u
t
-
f
ee
d
b
ac
k
r
eg
u
lato
r
b
ec
au
s
e
o
n
l
y
th
e
s
y
s
te
m
o
u
tp
u
t
is
a
v
ailab
l
e.
Fin
all
y
,
w
e
h
av
e
to
n
o
tice
th
at
t
h
e
p
r
o
b
lem
s
i
n
th
e
p
r
ese
n
t
p
ap
er
an
d
in
[
7
]
ar
e
q
u
ite
d
if
f
er
en
t
f
r
o
m
t
h
e
class
ical
co
n
tr
o
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
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8792
IJ
A
P
E
Vo
l.
6
,
No
.
2
,
A
u
g
u
s
t
2
0
1
7
:
63
–
72
64
p
r
o
b
lem
o
f
u
n
s
at
u
r
atin
g
o
u
t
p
u
t
s
y
s
te
m
s
i
n
p
r
ese
n
ce
o
f
in
p
u
t
s
at
u
r
atio
n
[
9
]
.
I
n
d
ee
d
,
in
th
e
p
r
o
b
le
m
o
f
co
n
tr
o
llin
g
o
u
tp
u
t
s
atu
r
ati
n
g
d
elay
ed
s
y
s
te
m
s
o
n
e
h
a
s
th
r
e
e
m
a
in
f
ea
t
u
r
es
d
escr
ib
in
g
th
e
clo
s
ed
-
lo
o
p
s
y
s
te
m
w
it
h
s
atu
r
at
in
g
r
eg
u
lato
r
:
(
1
)
th
e
s
y
s
te
m
is
n
o
n
l
in
ea
r
;
(
2
)
th
e
clo
s
ed
-
lo
o
p
s
y
s
te
m
m
a
y
b
e
as
y
m
p
to
ticall
y
g
lo
b
all
y
s
tab
le
ev
e
n
i
f
th
e
s
y
s
te
m
i
s
o
p
en
-
lo
o
p
s
tr
ictl
y
u
n
s
tab
le
at
th
e
o
r
ig
in
,
an
d
(
3
)
all
th
e
s
ig
n
al
s
o
f
th
e
clo
s
ed
-
lo
o
p
ar
e
b
o
u
n
d
ed
.
No
t
ice
th
at
in
th
e
s
at
u
r
ati
n
g
in
p
u
t
ca
s
e
th
e
s
y
s
te
m
o
u
tp
u
t
is
n
o
t
a
p
r
i
o
r
i
b
o
u
n
d
ed
,
f
o
r
th
i
s
,
t
h
e
s
y
s
te
m
s
h
o
u
ld
n
o
t
b
e
o
p
en
-
lo
o
p
s
tr
ictl
y
u
n
s
t
ab
le.
I
n
th
i
s
p
ap
er
w
e
ar
e
f
o
cu
s
i
n
g
t
h
is
co
n
tr
o
l
p
r
o
b
lem
o
f
s
y
s
te
m
s
w
i
th
s
at
u
r
atin
g
i
n
p
u
t
an
d
o
u
tp
u
t.
S
u
f
f
ici
en
t
co
n
d
itio
n
s
f
o
r
g
lo
b
al
s
tab
ilit
y
o
f
t
h
e
r
esu
lti
n
g
clo
s
ed
-
lo
o
p
s
y
s
te
m
ar
e
f
o
r
m
u
l
ated
u
s
i
n
g
i
n
p
u
t
-
o
u
tp
u
t s
tab
ilit
y
to
o
ls
[
9
]
-
[
1
0
]
.
T
h
ese
co
n
d
itio
n
s
w
ill
s
h
o
w
t
h
at
th
e
clo
s
ed
-
lo
o
p
s
y
s
te
m
i
s
as
y
m
p
to
ticall
y
g
lo
b
all
y
s
tab
l
e
alth
o
u
g
h
th
e
s
y
s
te
m
is
s
tr
ictl
y
u
n
s
tab
l
e.
T
h
is
p
ap
er
is
o
r
g
an
ized
a
s
f
o
llo
w
s
:
Sectio
n
2
is
d
e
v
o
te
d
to
f
o
r
m
u
late
t
h
e
co
n
tr
o
l
p
r
o
b
lem
;
th
e
co
n
tr
o
ller
d
esig
n
i
s
d
escr
ib
ed
in
Sectio
n
3
;
th
e
r
es
u
lti
n
g
clo
s
ed
-
lo
o
p
s
y
s
te
m
i
s
an
a
l
y
ze
d
in
Sectio
n
4
; th
e
co
r
r
esp
o
n
d
in
g
s
tab
ilizat
io
n
p
er
f
o
r
m
a
n
ce
s
a
r
e
illu
s
tr
ated
b
y
s
i
m
u
latio
n
in
Sectio
n
5
.
2.
CL
AS
S O
F
CO
NT
RO
L
SYS
T
E
M
T
h
e
in
p
u
t
-
o
u
tp
u
t r
ep
r
ese
n
tatio
n
o
f
a
s
at
u
r
ati
n
g
i
n
p
u
t
-
d
ela
y
ed
s
y
s
te
m
ca
n
b
e
m
o
d
eled
as f
o
ll
o
w
s
:
ˆ
ˆ
ˆ
(
)
1
(
)
(
)
(
)
(
)
s
x
s
A
s
y
s
B
s
e
u
s
(
1
.
1
)
w
it
h
(
)
(
,
(
)
)
M
y
t
s
a
t
y
x
t
(
1
.
2
)
1
1
10
()
n
nn
A
s
s
a
s
a
s
a
(
2
.
1
)
1
1
10
()
n
n
B
s
b
s
b
s
b
(
2
.
2
)
in
p
r
esen
ce
o
f
i
n
p
u
t c
o
n
s
tr
ai
n
t
:
()
M
u
t
u
(
3
)
w
h
er
e
(
u
(
t)
,
y
(
t)
)
ar
e
th
e
s
y
s
te
m
i
n
p
u
t
a
n
d
o
u
tp
u
t
an
d
(
û
(
s
)
,
ŷ
(
s
)
)
th
eir
L
ap
lace
tr
a
n
s
f
o
r
m
s
;
M
u
an
d
M
y
ar
e
t
w
o
r
ea
l p
o
s
itiv
e
co
n
s
tan
ts
.
I
t is f
u
r
th
er
as
s
u
m
ed
th
a
t:
A
1
.
A
(
s
)
is
H
u
r
w
itz
p
o
l
y
n
o
m
i
al,
A
2
.
(
s
A
(
s
)
,
B
(
s
)
)
ar
e
co
p
r
im
e.
No
te
th
at
i
n
t
h
e
ca
s
e
o
f
u
n
co
n
s
tr
ai
n
ed
o
u
tp
u
t
(
y
M
=
∞),
th
e
s
y
s
te
m
is
co
n
tr
o
llab
le
w
ith
a
lin
ea
r
s
tat
e
f
ee
d
b
ac
k
.
A
ls
o
,
A
(
s
)
is
n
o
t n
e
ce
s
s
ar
il
y
Hu
r
w
i
tz,
i.e
.
th
e
o
r
ig
in
ca
n
b
e
an
u
n
s
tab
le
eq
u
ilib
r
i
u
m
.
Fro
m
(
1
)
-
(
2
)
it’
s
ea
s
il
y
s
ee
n
t
h
at
t
h
e
s
y
s
te
m
i
s
ca
n
b
e
r
ep
r
esen
ted
ar
o
u
n
d
t
h
e
o
r
ig
in
b
y
t
h
e
lin
ea
r
ized
m
o
d
el:
ˆˆ
(
)
(
)
(
)
(
)
s
A
s
y
s
B
s
e
u
s
(
4
)
3.
CL
AS
S O
F
ST
AB
I
L
I
Z
I
N
G
RE
G
UL
AT
O
R
T
h
e
co
n
tr
o
l
d
esig
n
m
eth
o
d
is
th
e
f
in
ite
s
p
ec
tr
u
m
a
s
s
i
g
n
m
e
n
t
(
FS
A
)
w
h
ic
h
is
an
e
x
ten
s
i
o
n
to
tim
e
-
d
elay
s
y
s
te
m
s
ca
s
e
o
f
t
h
e
s
ta
n
d
ar
d
p
o
le
p
lace
m
e
n
t
d
esi
g
n
tech
n
iq
u
e.
T
h
e
s
tar
tin
g
s
tep
is
a
n
ar
b
itra
r
y
c
h
o
ice,
b
y
t
h
e
d
esi
g
n
er
,
o
f
a
p
air
o
f
H
u
r
w
itz
p
o
l
y
n
o
m
ial
s
o
f
t
h
e
f
o
r
m
:
`
1
1
1
0
1
1
1
0
(
)
,
(
)
.
.
.
nn
n-
nn
n
C
s
s
c
s
.
.
.
c
s
c
s
s
s
s
(
5
)
T
h
er
e
ex
is
ts
a
p
air
o
f
p
s
eu
d
o
-
p
o
ly
n
o
m
ia
ls
R
(
s
)
an
d
S
(
s
)
s
ati
s
f
y
i
n
g
t
h
e
B
ez
o
u
t e
q
u
atio
n
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
A
P
E
I
SS
N:
2252
-
8792
A
s
ymp
to
tic
S
ta
b
iliz
a
tio
n
o
f D
e
la
ye
d
S
ystems
w
ith
I
n
p
u
t a
n
d
Ou
tp
u
t S
a
tu
r
a
tio
n
s
(
A
d
el
Ma
h
jo
u
b
)
65
(
)
(
)
(
)
(
)
(
)
(
)
s
s
R
s
A
s
S
s
B
s
e
C
s
s
(
6
)
Fo
llo
w
i
n
g
t
h
e
p
o
le
p
lace
m
en
t
tech
n
iq
u
e
R
(
s
)
an
d
S
(
s
)
ar
e
th
e
u
n
iq
u
e
s
o
l
u
tio
n
o
f
t
h
e
B
ez
o
u
t
eq
u
atio
n
o
f
th
e
f
o
r
m
:
2
1
1
0
1
0
(
)
(
)
(
)
,
(
)
(
)
(
)
n
n
s
i
i
i
n
si
i
i
R
s
s
R
e
s
R
s
S
s
S
e
s
S
s
w
h
er
e
1
()
Rs
an
d
1
()
Ss
b
elo
n
g
to
G,
th
e
s
et
o
f
tr
a
n
s
f
er
f
u
n
ctio
n
s
o
f
d
is
tr
ib
u
ted
an
d
p
u
n
ct
u
a
l
d
elay
o
p
er
ato
r
s
(
A
p
p
en
d
ix
A
in
[
1
]
)
.
Fo
r
0
i
,
()
s
i
Re
an
d
()
s
i
Se
b
elo
n
g
to
[]
s
e
R
,
th
e
s
et
o
f
p
o
ly
n
o
m
ia
ls
i
n
s
e
.
Un
li
k
e
t
h
e
ca
s
e
o
f
n
o
n
-
d
ela
y
ed
s
y
s
te
m
s
,
th
e
(
f
i
n
ite
-
d
eg
r
ee
)
o
p
er
ato
r
s
R
(
s
)
a
n
d
S
(
s
)
ar
e
p
r
esen
tl
y
p
s
e
u
d
o
-
p
o
l
y
n
o
m
ials
an
d
,
co
n
s
eq
u
e
n
tl
y
,
ar
e
an
al
y
ti
ca
l f
u
n
ctio
n
s
o
f
s
.
As
d
e
g
(
)
(
)
2
1
s
S
s
B
s
e
n
,
it f
o
llo
w
s
th
at
d
e
g
(
s
A
(
s
)
R
(
s
)
)
=
d
eg
(
C
(
s
)
Ʌ
(
s
)
)
=
2n
w
h
ic
h
i
m
p
lies
t
h
at
d
eg
(
R
(
s
)
)
=
n
-
1
,
b
ec
au
s
e
d
e
g
(
(
)
)
1
s
A
s
n
an
d
f
u
r
t
h
er
m
o
r
e
as
()
s
A
s
an
d
(
)
(
)
C
s
s
ar
e
m
o
n
ic,
(
i.e
.
th
eir
h
ig
h
er
d
eg
r
ee
ter
m
co
e
f
f
icien
t
eq
u
als 1
)
.
W
ith
all
th
e
ab
o
v
e
n
o
tatio
n
s
,
th
e
s
at
u
r
ated
lin
ea
r
r
eg
u
lato
r
is
g
iv
e
n
t
h
e
alter
n
ati
v
e
f
o
r
m
:
(
)
(
)
(
)
ˆ
ˆ
ˆ
(
)
(
)
(
)
(
)
(
)
s
s
R
s
S
s
v
s
u
s
y
s
ss
(
7
.
1
)
ˆˆ
(
)
(
(
)
)
u
s
s
a
t
v
s
(
7
.
2
)
T
h
is
d
ef
in
ed
r
eg
u
lato
r
is
d
eter
m
i
n
ed
b
y
t
h
e
c
h
o
ice
o
f
th
e
p
o
l
y
n
o
m
ial
s
C
an
d
Ʌ.
W
e
ar
e
f
o
cu
s
i
n
g
o
n
th
e
f
o
llo
w
i
n
g
p
r
o
b
le
m
:
g
i
v
e
n
a
d
ela
y
e
d
s
y
s
te
m
(
1
-
3
)
a
n
d
a
r
e
g
u
la
to
r
(
7
)
,
b
ased
o
n
th
e
ch
o
ice
o
f
p
o
l
y
n
o
m
ials
C
an
d
Ʌ,
is
t
h
e
r
es
u
lti
n
g
clo
s
e
d
-
lo
o
p
s
y
s
te
m
g
lo
b
all
y
as
y
m
p
to
ticall
y
s
tab
le?
T
h
is
p
r
o
b
lem
is
r
elate
d
to
t
w
o
is
s
u
es:
a)
Do
es th
e
s
tab
iliz
in
g
r
eg
u
lato
r
,
f
o
r
a
g
iv
e
n
s
y
s
te
m
(
1
-
3
)
,
ex
i
s
t
?
b)
I
f
it d
o
es,
h
o
w
ca
n
w
e
d
esi
g
n
i
t?
T
o
o
u
r
k
n
o
w
led
g
e
t
h
ese
i
s
s
u
es
ar
e
n
o
t y
e
t so
v
ed
.
R
ema
r
ks:
(
i)
if
w
e
te
m
p
o
r
ar
ily
co
n
s
id
er
th
at
t
h
e
s
y
s
te
m
(
1
-
2
)
is
n
o
t
s
u
b
j
ec
t
to
th
e
co
n
s
tr
ain
t
(
3
)
,
i.e
.
(
u
M
=
∞).
T
h
en
,
th
e
ab
o
v
e
d
ef
i
n
ed
r
eg
u
lato
r
r
ed
u
ce
s
to
t
h
e
s
ta
n
d
ar
d
r
eg
u
lato
r
()
ˆˆ
(
)
(
)
()
Ss
u
s
y
s
s
R
s
.
I
f
w
e
h
av
e
al
s
o
y
M
=
∞,
th
e
n
t
h
e
clo
s
ed
-
lo
o
p
s
y
s
te
m
i
s
tr
an
s
f
o
r
m
ed
to
a
lin
ea
r
s
y
s
te
m
w
h
o
s
e
p
o
les ar
e
th
o
s
e
o
f
C
(
s
)
.
(
ii)
Fro
m
t
h
e
ab
o
v
e
s
y
s
te
m
a
n
d
r
eg
u
lato
r
,
it
f
o
llo
w
s
t
h
at
t
h
e
s
ig
n
al
s
v
(
t)
an
d
x
(
t)
ar
e
b
o
u
n
d
ed
w
h
ate
v
er
t
h
e
C
(
s
)
p
o
l
y
n
o
m
ial
’
s
c
h
o
ice.
So
f
r
o
m
(
1
-
2
)
an
d
(
7
)
,
it f
o
llo
w
s
,
f
o
r
all
t
,
th
at:
1
00
1
00
m
a
x
,
m
a
x
,
nn
jj
M
M
M
M
jj
jj
nn
M
M
j
M
j
M
jj
rs
v
u
u
y
x
y
b
u
a
y
(
8
)
iii)
Du
e
to
th
i
s
s
tr
u
ct
u
r
al
b
o
u
n
d
ed
n
es
s
,
s
o
m
e
u
n
s
tab
le
s
y
s
te
m
s
ca
n
b
e
g
lo
b
all
y
a
s
y
m
p
to
ti
ca
ll
y
s
tab
ilized
.
B
u
t
in
th
e
ca
s
e
o
f
u
n
co
n
s
tr
ai
n
ed
o
u
tp
u
t,
t
h
e
s
i
g
n
als
ar
e
n
o
t
a
p
r
io
r
i
b
o
u
n
d
ed
an
d
th
e
s
y
s
te
m
i
s
g
lo
b
all
y
s
tab
ilized
o
n
l
y
i
f
its
p
o
les ar
e
all
i
n
th
e
r
i
g
h
t
h
al
f
p
lan
e.
4.
CL
O
S
E
D
-
L
O
O
P
SYS
T
E
M
ANALY
SI
S
First,
let
u
s
p
o
in
t o
u
t a
s
ec
to
r
p
r
o
p
er
ty
f
o
r
th
e
s
at
u
r
atio
n
f
u
n
ctio
n
(
[
9
]
p
ag
e
4
1
7
)
.
L
E
M
M
A
1
C
o
n
s
id
er
an
ar
b
itra
r
y
p
o
s
iti
v
e
r
ea
l β a
n
d
a
r
ea
l f
u
n
ct
io
n
Φ
(
β,.
)
d
ef
in
ed
as
f
o
llo
w
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
IJ
A
P
E
Vo
l.
6
,
No
.
2
,
A
u
g
u
s
t
2
0
1
7
:
63
–
72
66
Φ
(
β,z)
=
z
–
s
at(
β,z)
f
o
r
an
y
r
ea
l z
(
9
.
1
)
th
en
,
f
o
r
an
y
z
[
-
z
M
,z
M
]
an
d
an
y
z
M
>
β o
n
e
h
as
:
2
0
.
(
,
)
z
z
z
w
h
er
e
M
M
z
z
(
9
.
2
)
w
h
ic
h
m
ea
n
s
t
h
at
Φ
(
β,.
)
b
elo
n
g
s
to
s
ec
to
r
[
0
β],
w
h
e
n
r
estric
ted
to
th
e
in
ter
v
al
[
-
z
M
,z
M
].
T
h
e
m
ai
n
r
es
u
lt is
d
escr
ib
ed
b
y
th
e
f
o
llo
w
i
n
g
t
h
eo
r
e
m
.
T
H
E
O
R
E
M
1
C
o
n
s
id
er
th
e
clo
s
ed
-
lo
o
p
co
n
tr
o
l
s
y
s
te
m
co
n
s
is
ti
n
g
o
f
s
y
s
te
m
(
1
-
2
)
s
u
b
m
it
ted
to
ass
u
m
p
tio
n
s
A
1
an
d
A
2
an
d
t
h
e
s
at
u
r
ated
r
eg
u
la
to
r
(
7
)
.
T
h
en
,
if
o
n
e
h
a
s
:
0
(
)
1
R
e
1
()
u
Aj
Cj
an
d
(
1
0
.
1
)
0
()
1
i
n
f
R
e
1
(
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(
)
im
y
Rj
C
j
j
(
1
0
.
2
)
2
2
0
1
(
)
(
)
1
γ
(
)
(
)
γγ
s
S
s
B
s
e
s
C
s
(
1
0
.
3
)
th
en
,
all
s
i
g
n
al
s
v(
t)
,
u
(
t)
,
x
(
t
)
an
d
y(
t
)
b
elo
n
g
to
L
2
.
w
h
er
e
γ
p
is
th
e
L
p
-
g
ai
n
o
f
a
n
L
p
-
s
tab
le
o
p
er
ato
r
.
,
,
(
)
(
)
(
)
M
M
M
M
u
y
r
e
i
m
MM
v
u
x
y
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j
R
j
R
vx
(
1
1
.
1
)
2
(
)
(
)
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(
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(
(
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(
)
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.
/
2
i
u
A
s
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s
C
s
A
s
C
s
(
1
1
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2
)
2
(
)
(
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γγ
(
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(
(
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(
)
)
.
/
2
ii
y
R
s
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s
C
s
R
s
C
s
(
1
1
.
3
)
01
1
γ
/
2
1
γ
/
2
γ
,
γ
1
γ
/
2
1
γ
/
2
y
i
i
ui
uy
u
i
y
i
i
(
1
1
.
4
)
I
n
t
h
e
s
eq
u
el,
t
h
e
n
o
tatio
n
s
will
b
e
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i
m
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li
f
ied
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y
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iti
n
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licitl
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en
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ly
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o
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ia
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n
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p
s
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o
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p
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ial
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.
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l
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o
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e’
ll
a
v
o
id
th
e
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y
m
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o
l
“
^”
f
o
r
th
e
L
ap
lac
e
tr
an
s
f
o
r
m
s
u
n
le
s
s
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ec
es
s
ar
y
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h
u
s
,
d
ep
en
d
in
g
o
n
th
e
co
n
tex
t,
t
h
e
letter
x
w
ill
b
e
eith
er
th
e
s
i
g
n
al
x
(
t)
o
r
its
L
ap
lace
tr
an
s
f
o
r
m
.
P
RO
O
F
:
L
et
u
s
d
ef
i
n
e
t
h
ese
n
e
w
e
r
r
o
r
s
:
,
v
v
u
x
x
y
(
1
2
)
B
y
co
n
s
id
er
in
g
all
t
h
e
ab
o
v
e
n
o
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n
s
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eq
u
atio
n
s
(
1
)
an
d
(
7
.
1
)
ar
e
w
r
itte
n
as
f
o
llo
w
s
:
s
R
S
v
u
y
(
1
3
.
1
)
s
x
A
y
B
e
u
(
1
3
.
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
A
P
E
I
SS
N:
2252
-
8792
A
s
ymp
to
tic
S
ta
b
iliz
a
tio
n
o
f D
e
la
ye
d
S
ystems
w
ith
I
n
p
u
t a
n
d
Ou
tp
u
t S
a
tu
r
a
tio
n
s
(
A
d
el
Ma
h
jo
u
b
)
67
Mu
ltip
l
y
i
n
g
b
y
-
A
b
o
th
s
id
e
s
o
f
(
1
3
.
1
)
,
o
n
e
h
as:
s
A
R
A
S
A
v
u
y
No
w
,
o
p
er
atin
g
S/Ʌ
o
n
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th
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i
d
es o
f
(
1
3
.
2
)
y
ield
s
s
S
S
A
S
B
x
y
e
u
Usi
n
g
(
6
)
,
ad
d
in
g
th
e
s
e
t
w
o
la
s
t e
q
u
atio
n
s
g
i
v
e
s
S
x
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v
C
u
(
1
4
)
Usi
n
g
t
h
e
f
ac
t t
h
at
u
v
v
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d
r
ea
r
r
a
n
g
i
n
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ter
m
s
,
o
n
e
h
a
s
:
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A
S
v
v
x
CC
(
1
4
)
ca
n
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e
e
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u
iv
ale
n
tl
y
w
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itte
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as
f
o
llo
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s
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A
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v
v
x
CC
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1
5
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w
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er
e
1
is
a
tr
an
s
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er
f
u
n
ctio
n
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s
ig
n
al
ar
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r
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it
ial
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n
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itio
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As C
a
n
d
Ʌ ar
e
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r
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itz,
1
v
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p
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h
ich
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m
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lies
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a
t
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.
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er
atin
g
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Be
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n
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th
s
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f
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1
3
.
1
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d
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ield
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s
s
s
s
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e
v
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u
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6
.
1
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er
atin
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n
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th
s
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f
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3
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2
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d
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ld
s
s
s
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A
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B
x
s
y
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e
u
(
1
6
.
2
)
Usi
n
g
(
1
2
)
,
ad
d
in
g
(
1
6
.
1
)
an
d
(
1
6
.
2
)
g
iv
es:
2
s
C
s
R
B
x
x
e
v
CC
(
1
7
)
w
h
er
e
22
L
.
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q
u
atio
n
s
(
1
5
)
an
d
(
1
7
)
a
r
e
r
e
p
r
esen
ted
b
y
Fi
g
u
r
e
1
as th
e
s
y
s
te
m
w
it
h
f
ee
d
b
ac
k
s
b
elo
w
w
h
er
e:
11
S
Ux
C
;
22
s
B
U
e
v
C
T
h
is
s
y
s
te
m
co
n
s
i
s
ts
o
f
a
m
ai
n
f
ee
d
b
ac
k
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n
d
t
w
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n
ter
n
al
f
e
ed
b
ac
k
s
,
r
ef
er
r
ed
to
as
f
ee
d
b
ac
k
s
F1
an
d
F2
.
T
h
e
w
h
o
le
s
y
s
te
m
s
tab
ilit
y
an
al
y
s
is
w
ill b
e
d
o
n
e
in
t
h
r
e
e
s
tep
s
.
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tep
1
:
s
ta
b
ilit
y
o
f f
ee
d
b
a
ck
F
1
:
T
h
e
f
o
r
w
ar
d
p
ath
w
a
y
o
f
th
i
s
f
ee
d
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ac
k
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lin
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ti
m
e
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i
n
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ar
ian
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te
m
w
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th
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a
n
s
f
er
f
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n
ctio
n
(A
-
C
)
/
C
.
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h
e
r
etu
r
n
p
ath
w
a
y
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t
h
e
n
o
n
lin
ea
r
o
p
er
ato
r
Φ
(
u
M
,
.
)
w
h
ich
,
u
s
i
n
g
le
m
m
a
1
,
b
elo
n
g
s
to
[
0
,
α
u
]
.
Usi
n
g
th
e
cir
cle
cr
iter
io
n
[
9
]
–
[
15
]
,
o
n
e
ca
n
g
et
t
h
a
t
F1
is
L
2
-
s
tab
l
e
if
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
IJ
A
P
E
Vo
l.
6
,
No
.
2
,
A
u
g
u
s
t
2
0
1
7
:
63
–
72
68
02
(
)
(
)
1
i
n
f
R
e
()
u
A
j
C
j
Cj
(
1
8
.
1
)
No
w
,
let
co
n
s
id
er
th
e
o
p
er
ato
r
G
1
s
u
ch
t
h
at
11
(
)
(
)
v
t
G
U
t
.
T
h
en
,
if
w
e
ap
p
l
y
th
e
lo
o
p
tr
an
s
f
o
r
m
atio
n
th
eo
r
e
m
(
[
2
]
p
ag
es 3
4
1
-
3
4
3
)
,
w
e
ca
n
ea
s
il
y
g
et
th
e
L
2
-
g
ai
n
o
f
G
1
a
s
f
o
llo
ws:
21
1
/
2
γ
(
)
1
/
2
iu
u
iu
G
(
1
8
.
2
)
w
h
ic
h
is
n
o
th
i
n
g
b
u
t
0
.
S
tep
2
:
s
ta
b
ilit
y
o
f fe
e
d
b
a
ck
F
2
:
I
n
a
s
i
m
ilar
m
a
n
n
er
,
o
n
e
ca
n
s
h
o
w
th
at
F2
is
L
2
-
s
tab
le
i
f
02
(
)
(
)
(
)
1
i
n
f
R
e
(
)
(
)
y
C
j
j
j
R
j
C
j
j
(
1
8
.
3
)
Fu
r
t
h
er
m
o
r
e,
let
G2
d
en
o
te
th
e
o
p
er
ato
r
22
(
)
(
)
x
t
G
U
t
s
u
c
h
t
h
at
1
22
1
/
2
γ
(
)
γ
1
/
2
i
i
y
y
i
i
y
G
(
1
8
.
4
)
S
tep
3
:
Ma
i
n
feed
b
a
ck
s
ta
b
ilit
y:
ap
p
ly
i
n
g
t
h
e
s
m
all
g
ai
n
th
e
o
r
em
o
n
Fig
u
r
e
1
,
it
f
o
llo
w
s
t
h
at
th
is
f
ee
d
b
ac
k
is
L
2
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s
tab
le
p
r
o
v
id
ed
th
at
2
1
2
2
2
2
γ
(
)
γ
(
)
γ
1
s
SB
G
G
e
C
w
h
ic
h
i
s
n
o
th
i
n
g
b
u
t
t
h
e
co
n
d
itio
n
(
1
0
.
3
)
.
T
h
en
i
t
f
o
llo
w
s
th
at
12
,,
U
U
x
an
d
v
b
elo
n
g
to
L
2
a
s
1
2
2
,
L
.
Fin
all
y
,
s
i
n
ce
f
ee
d
b
ac
k
s
F1
a
n
d
F2
ar
e
L
2
-
s
tab
le,
w
e
d
ed
u
ce
f
r
o
m
(
1
5
)
an
d
(
1
7
)
th
at
2
xL
an
d
2
vL
.
RE
M
ARK
S
a)
I
n
ca
s
e
w
h
er
e
co
n
d
itio
n
s
(
1
0
.
1
)
an
d
(
1
0
.
2
)
h
o
ld
,
th
e
g
lo
b
al
as
y
m
p
to
tic
s
tab
ilit
y
at
t
h
e
o
r
ig
in
is
g
u
ar
an
teed
.
R
ec
all
t
h
at
all
t
h
e
s
i
g
n
al
s
a
r
e
b
o
u
n
d
ed
i.e
.
,,
M
M
M
u
u
y
y
v
v
an
d
M
xx
.
T
h
en
g
lo
b
al
s
tab
ilit
y
m
ea
n
s
t
h
at
all
s
ig
n
al
s
co
n
v
er
g
e
to
ze
r
o
f
o
r
all
in
itia
l
co
n
d
itio
n
s
.
b
)
T
h
e
d
esig
n
p
r
o
ce
d
u
r
e
o
f
th
e
s
tab
ilizi
n
g
r
eg
u
la
to
r
co
u
ld
b
e
co
m
p
o
s
ed
o
f
th
r
ee
s
tep
s
w
h
ic
h
ar
e:
ch
o
o
s
in
g
p
o
ly
n
o
m
ia
ls
C
an
d
Ʌ,
s
o
l
v
i
n
g
B
ez
o
u
t
eq
u
atio
n
(
6
)
an
d
co
m
p
u
ti
n
g
p
s
e
u
d
o
-
p
o
l
y
n
o
m
ials
R
a
n
d
S
an
d
f
i
n
all
y
ch
ec
k
i
n
g
co
n
d
itio
n
s
(
1
0
.
1
)
an
d
(
1
0
.
2
)
.
I
f
th
ese
h
o
l
d
k
ee
p
th
e
o
b
tain
ed
r
eg
u
lato
r
.
E
ls
e,
m
a
k
e
a
d
if
f
er
e
n
t c
h
o
ice
o
f
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an
d
g
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k
to
s
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n
d
s
tep
.
c)
A
lt
h
o
u
g
h
co
n
d
itio
n
s
(
1
0
.
1
)
an
d
(
1
0
.
2
)
d
o
n
o
t
allo
w
ch
ar
ac
ter
izatio
n
o
f
s
tab
ilizab
le
s
y
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te
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s
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in
ter
m
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o
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ze
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.
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o
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ts
id
e
th
e
lef
t
h
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p
la
n
e.
T
h
is
is
ill
u
s
tr
ated
b
y
t
h
e
ex
a
m
p
le
i
n
s
ec
tio
n
s
i
m
u
latio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
A
P
E
I
SS
N:
2252
-
8792
A
s
ymp
to
tic
S
ta
b
iliz
a
tio
n
o
f D
e
la
ye
d
S
ystems
w
ith
I
n
p
u
t a
n
d
Ou
tp
u
t S
a
tu
r
a
tio
n
s
(
A
d
el
Ma
h
jo
u
b
)
69
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
a
m
o
f
t
h
e
f
ee
d
b
ac
k
s
y
s
te
m
d
escr
ib
ed
b
y
eq
u
atio
n
s
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1
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I
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A
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6.
CO
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tab
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d
.
RE
F
E
R
E
NC
E
S
[1
]
T
a
rb
o
u
riec
h
S
.
,
G
a
rc
ia
G
.
,
G
lat
tf
e
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e
r
A
.
H.
,
"
A
d
v
a
n
c
e
d
stra
teg
ies
in
c
o
n
t
ro
l
sy
ste
m
s
w
it
h
in
p
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t
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n
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o
u
tp
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c
o
n
stra
in
ts
,"
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NCI
S
,
V
o
l.
3
4
6
,
S
p
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e
r,
2
0
0
7
.
[2
]
Bo
h
y
u
n
g
L
e
e
a
n
d
Ja
n
g
Gy
u
Lee
,
"
Ro
b
u
st
c
o
n
tr
o
l
o
f
u
n
c
e
rtai
n
sy
ste
m
s
w
it
h
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p
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t
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a
n
d
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n
p
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t
se
c
to
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n
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li
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e
a
rit
y
,
"
Pro
c
e
e
d
in
g
s
o
f
t
h
e
3
9
t
h
IEE
E
C
o
n
fer
e
n
c
e
o
n
De
c
isio
n
a
n
d
Co
n
tro
l
(
Ca
t.
N
o
.
0
0
CH3
7
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8
7
)
,
S
y
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n
e
y
,
NSW
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2
0
0
0
,
p
p
.
4
4
3
0
-
4
4
3
5
v
o
l.
5
.
[3
]
M
a
h
jo
u
b
,
F
.
G
iri
,
V
.
V
a
n
A
ss
c
h
e
,
F
.
Z.
Ch
a
o
u
i,
"
T
ra
c
k
in
g
P
e
rf
o
r
m
a
n
c
e
Ac
h
iev
e
m
e
n
t
f
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r
Co
n
ti
n
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o
u
s
-
T
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m
e
De
la
y
e
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e
m
s
S
u
b
jec
t
to
A
c
tu
a
to
r
S
a
tu
r
a
ti
o
n
a
n
d
Ou
t
p
u
t
Distu
rb
a
n
c
e
s,"
Asia
n
J
o
u
rn
a
l
o
f
Co
n
tro
l
,
v
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l.
1
7
,
n
o
.
5
,
p
p
.
1
–
7
,
S
e
p
tem
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e
r
2
0
1
4
.
[4
]
Zh
o
u
B.
,
L
in
Z.
,
L
a
m
J
.
,
"
S
e
m
i
-
g
lo
b
a
l
sta
b
il
iza
ti
o
n
o
f
li
n
e
a
r
ti
m
e
-
d
e
la
y
s
y
ste
m
s
w
it
h
c
o
n
tro
l
e
n
e
rg
y
c
o
n
stra
in
t,
"
A
u
to
m
a
ti
c
a
,
v
o
l.
4
8
,
n
o
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4
,
p
p
.
6
9
4
–
6
9
8
,
A
p
ril
2
0
1
2
.
[5
]
A
.
M
a
h
jo
u
b
,
F
.
G
iri
,
N.
De
rb
e
l,
"
De
la
y
e
d
s
y
ste
m
c
o
n
tro
l
in
p
re
se
n
c
e
o
f
a
c
tu
a
to
r
sa
tu
ra
ti
o
n
”
,
Al
e
x
a
n
d
r
i
a
En
g
i
n
e
e
rin
g
J
o
u
rn
a
l
,
v
o
l.
5
3
,
n
o
.
3
,
p
p
.
5
5
3
-
5
6
1
,
S
e
p
tem
b
e
r
2
0
1
4
.
[6
]
A
.
M
a
h
jo
u
b
,
N.
De
rb
e
l,
"
De
lay
e
d
S
y
ste
m
Co
n
tro
l
i
n
P
re
se
n
c
e
o
f
M
a
g
n
it
u
d
e
a
n
d
Ra
te
S
a
tu
ra
ti
o
n
,
"
In
ter
n
a
ti
o
n
a
l
Rev
iew o
f
Au
t
o
ma
t
ic Co
n
tro
l
,
v
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l
.
7
,
n
o
.
3
,
p
p
.
3
0
7
-
3
1
6
,
2
0
1
4
.
[7
]
L
iu
,
D.,
&
M
ich
e
l
,
A
.
N
.
,
"
Dy
n
a
m
i
c
a
l
s
y
ste
m
s
w
it
h
sa
tu
ra
ti
o
n
n
o
n
l
in
e
a
rit
ies
:
A
n
a
ly
sis
a
n
d
d
e
sig
n
,"
Be
rli
n
:
S
p
rin
g
e
r,
p
p
.
3
7
-
4
9
,
1
9
9
4
.
[8
]
Ch
a
o
u
i
F
.
Z,
G
iri
F
.
,
M
’S
a
a
d
M
.
,
"
A
d
a
p
ti
v
e
c
o
n
tro
l
o
f
in
p
u
t
-
c
o
n
stra
in
e
d
ty
p
e
-
1
p
lan
ts:
sta
b
il
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ti
o
n
a
n
d
trac
k
in
g
,
"
Au
to
ma
ti
c
a
,
v
o
l.
3
7
,
p
p
.
1
9
7
-
2
0
3
,
2
0
0
1
.
[9
]
V
id
y
a
sa
g
a
r
M
.
,
No
n
li
n
e
a
r S
y
ste
m
s A
n
a
lys
is
,
S
IA
M
,
P
A
,
USA
,
2
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