EE 453
HMWK 2
1. If A can be diagonalized, find a nonsingular T such that T 1 AT is diagonal.
3 3 1
0
0
(a) A = 1
0
1
0
3 1
3
2
(b) A = 2 1
2
1 2
5 1 0
(c) A = 8 0 1
6 0 0
2. For the matrices of of Question 1, compute eA(tt0 ) .
3. For the matrices of

EE 453
Homework 1
(s2)
1. Find a realization of the transfer function g(s) = s3 s
2 s2 . Is your realization minimal?
If not, find a minimal realization of this transfer function. Find the Gilberts realization for
g(s). Is it a minimal realization. Whay?

LINEAR
SYSTEMS
THEORY
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LINEAR
SYSTEMS
THEORY
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Published by Princeton University Press, 41 William Street,

December 14, 2015
EE 453
Homework # 7
1. Consider
1
x = 0
1
1 2
1
0 1 x + 0 u
1 1
1
First show that (A, b) is a controllable pair and then find a state feedback
matrix k so that |sI (A bk)| = s3 + 3s2 + 3s + 1.
2. Consider the realization below:
1 1
1
1
1

November 29, 2015
EE 453
Homework # 6
1. Find an input that drives the state x(1) = 2 to x(3) = 5 for the realization x0 = 3x + u ; y = 2x. What will be the input that you will use if
you would like to have x(3) = 2? Can you find an input that results in

1
EE 453
HMWK 1
1. Use the field axioms to show that, in any field, the additive identity
and the multiplicative identity are unique.
2. Show that in any vector space, the zero is unique (by zero, we mean
the identity element with respect to the vector ad