ECE 531
LINEAR SYSTEM THEORY
SPRING 2006
Takehome Examination #1
Due: Monday, 13 March 2006 at 11:00am
This is a takehome exam; open book, open notes.
Please list on the exam paper all
outside sources (books, notes, etc.) which you consulted in working the problems.
You are
to work independently
, but feel free to contact me should you have any questions.
1. For ˙
x
(
t
) =
Ax
(
t
), we know that
x
(0) =
1
2
1
implies
x
(
t
) =
1
2
1
e

2
t
,
that
x
(0) =
1
1
1
implies
x
(
t
) =
1
1
1
e

3
t
,
and that
x
(0) =
2
0
1
implies
x
(
t
) =
2
0
1
e

t
,
What is
A
? Indicate whether or not more than one choice of
A
is possible, and if so
provide all possible choices.
2. For ˙
x
(
t
) =
Ax
(
t
), we know that
x
(0) =
•
2
1
‚
implies
x
(
t
) =
•
2
1
‚
e

2
t
and that
x
(0) =
•
3
2
‚
implies
x
(
t
) =
•
3 + 2
t
2 +
t
‚
e

2
t
.
What is
A
? Indicate whether or not more than one choice of
A
is possible, and if so
provide all possible choices.
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 Spring '07
 Williamson
 Derivative, state transition matrix

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