enee 660 hw sol #5
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8/3/2019 ENEE 660 HW Sol #5
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Electrical and Computer Engineering Department
University of Maryland College Park
ENEE 660
System Theory
Fall 2008
Professor John S. Baras
Solutions to Homework Set #5
Problem 1
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Problem 2
Problem 3
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So the answer to (a) is that =3.
And this construction provides the answer to (c).
To answer (b) we have from above that the least common multiple of the denominators of the
elements of is d(s) = (s + 1)(s + 2). So following Theorem 5.5.38, =N(s) /d(s), where
2 2( 2)( )
1 1
s sN s
s
+ + = +
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Then the g.c.d.s of the subdeterminants ofN(s) are
D1(s) = 1
D2(s) = (s +2)(s +1) + 2 (s +2) = (s +2)(s +3)
And therefore the Smith form ofN
(s) is
Therefore the McMillan canonical form of is then
So the poles (three) of are -1, -1, -2, while there is only one zero at -3.
Problem 4
1 0( )
0 ( 2)( 3)N s
s s
+ +
10
( 1)( 2)( )( 3)
0
( 1)
s sT s
s
s
+ +
+
+
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Problem 5
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Problem 6
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