Massachusetts
Institute
of
Technology
Department
of
Electrical
Engineering
and
Computer
Science
6.243j
(Fall
2003):
DYNAMICS
OF
NONLINEAR
SYSTEMS
by
A.
Megretski
Problem
Set
1
1
Problem
1.1
Behavior
set
B
of
an
autonomous
system
with
a
scalar
binary
DT
output
consists
of
all
DT
signals
w
=
w
(
t
)
→ {
0
,
1
}
which
change
value
at
most
once
for
0
�
t
<
�
.
(a)
Give
an
example
of
two
signals
w
1
, w
2
→
B
which
commute
at
t
=
3,
but
do
not
define
same
state
of
B
at
t
=
3.
(b)
Give
an
example
of
two
different
signals
w
1
, w
2
→ B
which
define
same
state
of
B
at
t
=
4.
(c)
Find
a
timeinvariant
discretetime
finite
statespace
“difference
inclusion”
model
for
B
,
i.e.
find
a
finite
set
X
and
functions
g
:
X
∈�
{
0
,
1
}
,
f
:
X
∈�
S
(
X
),
where
S
(
X
)
denotes
the
set
of
all
nonempty
subsets
of
X
,
such
that
a
sequence
w
(0)
, w
(1)
, w
(2)
, . . .
can
be
obtained
by
sampling
a
signal
w
→ B
if
and
only
if
there
exists
a
sequence
x
(0)
, x
(1)
, x
(2)
, . . .
of
elements
from
X
such
that
x
(
t
+
1)
→
f
(
x
(
t
))
and
w
(
t
)
=
g
(
x
(
t
))
for
t
=
0
,
1
,
2
,
. . . .
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 AlexandreMegretski
 Dynamics, Constant of integration, Empty set, Vector Motors, Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science

Click to edit the document details