6.241 Spring 2011
Midterm Exam
March 27, 2011
Problem 1
Let A Cnn , and B Cmm . Show that X (t) = eAt X (0)eBt is the solution to X =
AX + X B .
1
Solution Recalling the denition of matrix exponential
6.241 Spring 2011
Final Exam
5/16/2011, 9:00am 12:00pm
The test is open books/notes, but no collaboration is allowed: i.e., you should not
discuss this exam or solution approaches with anybody, except
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.241: Dynamic SystemsSpring 2011
Homework 10 Solutions
Exercise 23.1 a) We are given the single input L
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.241: Dynamic SystemsSpring 2011
Homework 9 Solutions
Exercise 21.1 We can use additive perturbation mo
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.241: Dynamic SystemsSpring 2011
Homework 8 Solutions
Exercise 17.4 1) First, in order for the closed l
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.241: Dynamic SystemsSpring 2011
Homework 7 Solutions
Exercise 15.1 (a) The system is causal if the imp
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.241: Dynamic SystemsFall 2008
Homework 6 Solutions
Exercise 13.1 (a) The system described by
x=z
z = 4
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.241: Dynamic SystemsSpring 2011
Homework 5 Solutions
Exercise 7.2 a) Suppose c = 2. Then the impulse r
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.241: Dynamic SystemsSpring 2011
Homework 4 Solutions
Exercise 4.7 Given a complex square matrix A, the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.241: Dynamic SystemsFall 2007
Homework 3 Solutions
Exercise 3.2 i) We would like to minimize the 2-nor
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.241: Dynamic SystemsFall 2007
Homework 2 Solutions
Exercise 1.4 a) First dene all the spaces:
R(A) = c
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.241: Dynamic SystemsSpring 2011
Homework 1 Solutions
Exercise 1.1 a) Given square matrices A1 and A4 ,