ME540/ECE515 HW#1 Solutions
1. Depicted below is a Pendubot with massless links, and masses at their ends. As in the course
notes a torque is applied at the base of the rst link, and is available for control.
The equations of motion for the system are giv

ECE515-ME540: Assignment #4
Due: Apr 2
Instructor: Geir E. Dullerud
Problems:
1. Given > 0 dene the subset of the complex numbers C = cfw_z C : Re(z) < . Prove that if
eig(A) C and Q is a positive denite matrix, then there is a unique positive denite solu

ECE515-ME540: Assignment #3
Due: Mar 12
Instructor: Geir E. Dullerud
Problems:
1. Given arbitrary constants a, b, and the matrix
(a 1)
1
0
(1 + a)
0 .
A = 1
1
(1 + a b) b
(a) Determine the eigenvalues of this matrix.
(b) Find 3 linearly independent genera

ECE515-ME540: Assignment #2
Due: Feb 19
Instructor: Geir E. Dullerud
Problems:
(1) Complete exercise 2.11.10 in the course notes.
(2) Complete exercise 2.11.19 in course notes.
(3) Jordan decomposition. In some sense, matrices that have non-scalar Jordan

ECE515-ME540: Assignment #1
Due: Feb 5
Instructor: Geir E. Dullerud
Problems:
(1) Depicted below is a Pendubot with massless links, and masses at their ends. As in the course notes a
torque is applied at the base of the rst link, and is available for cont

ECE 550 Final Exam
Instructions: This is an closed-book, closed-notes exam. Only 2 8.5x11 crib sheets are
allowed during the exam. Moreover, calculators, computers and other electronic aids are not
allowed in this exam. Please make sure to state your assu

ME 540/ECE515 Midterm - Spring 2011
Name:
A table of Laplace transforms and other useful formulas appears on the last page of this
booklet. If you separate the other pages of this book, write your name on every page. Calculators are not allowed. The point