University of California, Santa Barbara
Department of Electrical & Computer Engineering
ECE 147b: Digital Control
Winter 2009
Homework 3.
Due 5.00pm Friday, 20th February, 2009 in the homework boxes on the 3rd. floor of Harold
Frank Hall.
If you use
Matlab
to solve any part of the homework, you must attach a copy of the
Matlab
script to
your homework to get any credit for the problem.
Problem 1.
Consider two discretetime statespace systems,
P
1
(
z
) =
bracketleftbigg
A
1
B
1
C
1
D
1
bracketrightbigg
,
and
P
2
(
z
) =
bracketleftbigg
A
2
B
2
C
2
D
2
bracketrightbigg
.
Each of these systems has more than one input and output. The number of poles in
P
1
(
z
) is
n
1
and the
number of poles in
P
2
(
z
) is
n
2
. Calculate a statespace realization for each of the following interconnections.
The “
A
” matrix of your realization must not have dimension greater than
n
1
+
n
2
.
a)
P
1
(
z
) +
P
2
(
z
). Also sketch this as a block diagram with two blocks (
P
1
(
z
) and
P
2
(
z
)). What are the
relationships between the numbers of inputs and outputs of
P
1
(
z
) and
P
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 Winter '08
 Staff
 p1, Harold Frank Hall, discretetime statespace systems, following discretetime state

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