ECEN 5448 Fall 2006 Final Exam
Professor D. G. Meyer
Saturday, December 16, 2006. 1:30pm - 4:00pm
Instructions: This is a closed-book exam. You may use only your formula sheets.
Work on your own paper, and please:
Begin each numbered problem on a new she

ECEEN 5448 Fall 2011 Homework #4
Professor David G. Meyer
November 10, 2011. Due: Novemeber 29, 2011
1. Consider the state-space realization
A=
0 1
0 0
; b=
0
1
;c =
1 0
which describes, of course, a free mass (in normalized units) with input being a forc

ECEEN 5448 Fall 2011 Homework #3
Professor David G. Meyer
October 25, 2011. Due: Novemeber 8, 2011
1. Recall that a square matrix Q is symmetric if Q = QT . We present the following facts without
proof for symmetric matrices that you can assume as given:

ECEEN 5448 Fall 2011 Homework #1 Solutions
Professor David G. Meyer
September 26, 2011
1. In class, we argued the rationale for the following denition of the dimension of a vector
space:
Denition 0.1 Let V be a vector space. dimV = N if, and only if we ca

ECEEN 5448 Fall 2011 Homework #1
Professor David G. Meyer
September 12, 2011.
Due: September 22, 2011
1. In class, we argued the rationale for the following denition of the dimension of a vector
space:
Denition 0.1 Let V be a vector space. dimV = N if, an

ECEEN 5448 Fall 2011 Homework #2 Solutions
Professor David G. Meyer
October 11, 2011
1. Show that cfw_A, b, c and cfw_T 1 AT, T 1b, cT where T is any non-singular square matrix (of
the proper size) realize the same transfer function.
This is a straightfo

ECEEN 5448 Fall 2011 Homework #5 Solutions
Professor David G. Meyer
December 8, 2011
1. Consider the 1-dimensional time-varying linear system
x = t (u x)
(a) Find the state-transition matrix, (t, ).
Here A(t) = t. Since the A-matrix is a scalar, of course

ECEEN 5448 Fall 2011 Homework #4 Solutions
Professor David G. Meyer
Novemeber 29, 2011
1. The state-space realization is
A=
0 1
0 0
; b=
0
1
;c =
1 0
which describes, of course, a free mass (in normalized units) with input being a force on the
mass and ou

ECEEN 5448 Fall 2011 Homework #3 Solutions
Professor David G. Meyer
Novemeber 8, 2011
1. Recall that a square matrix Q is symmetric if Q = QT . We present the following facts without
proof for symmetric matrices that you can assume as given:
Their eigenv

ECEN 5448 Midterm Exam Fall 2011
Professor D. G. Meyer
October 15, 2011
Instructions: This is a restricted open-book exam. You can consult your class notes,
any texts, formula sheets, graded HW and HW solutions. You cannot consult the
internet.
Do the exa

ECEN 5448 Midterm Exam Solutions
Fall 2011
Professor D. G. Meyer
October 21, 2011
1. (a) Prove the following theorem.
Theorem 0.1 If cfw_A, b is controllable there is a row vector c that makes cfw_A, c observable.
If A, b is controllable, there is a squar

ECEEN 5448 Fall 2011 Homework #2
Professor David G. Meyer
September 30, 2011.
Due: October 11, 2011
1. Show that cfw_A, b, c and cfw_T 1 AT, T 1b, cT where T is any non-singular square matrix (of
the proper size) realize the same transfer function.
2. De

ECEEN 5448 Fall 2011 Homework #5
Professor David G. Meyer
Due: December 8, 2011
1. Consider the 1-dimensional time-varying linear system
x = t (u x)
(a) Find the state-transition matrix, (t, ).
(b) Given x(0) = 1 and u(t) = 1 for t 0, nd x(t) for t 0.
2.