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Assignment #21
ECSE2410 Signals & Systems  Spring 2009
Due Fri 04/17/09
1(30). Use the Routh array as discussed in class to determine the number of roots that the following
polynomials have in the right half of the splane, if any.
Note that (c) requires the special case of the
Routh array where a 0 is replaced by a small positive number
ε
.
Use the
roots
command in Matlab to
check your answers.
(a)
s
4
+ s
3
+ 2s
2
+ 5s + 8
(b)
s
5
+ s
4
+ 2s
3
+ s + 5
(c)
s
5
+ 2s
4
+ 2s
3
+ 4s
2
+ 11s + 10
2(10).
For the polynomial.
, use the Routh array to determine the range of
()
K
s
s
s
s
s
p
+
+
+
+
=
2
3
2
3
4
such that all roots have negative real parts.
Use Matlab to verify your bounding (between right
0
>
K
and left half planes) value of
K
i.e., substitute your bounding
K
into Matlab
roots
and show that the
resulting roots of
contain a pair of
()
s
p
axis
j
−
ω
roots and two real roots that have negative real parts.
3(30).
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