ECE 531
LINEAR SYSTEM THEORY Take-home Examination #2 Due: Thursday, 4 May 2006 at 6:25pm (in class)
SPRING 2006
This is a take-home exam; open book, open notes. Please list on the exam paper all outside sources (books, notes, etc.) which you cons
ECE 531
LINEAR SYSTEM THEORY
HOMEWORK ASSIGNMENT #3
Due: 28 October 2014
FALL 2014
1. Determine whether or not the following homogeneous state equations are (marginally)
stable, and whether or not they are asymptotically stable.
(a) The continuous-time sy
Appendix A
State Space Tutorial
Gantry Crane: An Example
The following gure shows a gantry crane with one degree of freedom for the cart. The mass of the load is assumed
to be concentrated and equal to m. The combined mass of the cart and the pulley is M
Electrical and Computer Engineering Department
Linear System Analysis, ECE531 (Spring 2011)
Midterm
Wednesday, March 9, 2011
Name:
You have one hour fifteen minutes.
Problem
Please show enough (neat) work in the clear spaces remaining for the
problems to
Electrical and Computer Engineering Department
Linear System Analysis, ECE531 (Spring 2008)
Midterm I
Tuesday, April 01, 2008
Name:
You have one hour fifteen minutes.
Problem
Please show enough (neat) work in the clear spaces remaining for the
problems to
ECE531 Project Phase Tow
Please prepare a preliminary report and e-mail it to me by April 15, 2013. This report
should contain the following:
Phase One
1. A description of your system and its mathematical model, i.e., the differential
equations governing
ECE531 Project
The goal of the project associated with ECE531 is to let you apply what you learn in the
course to the system of your choice. You have already chosen a system and during the
semester you have submitted two progress reports on the assigned t
Electrical and Computer Engineering Department
Linear System Analysis, ECE531 (Spring 2009)
Final
Tuesday, May 12, 2009
ame:
Please do preliminary calculations in the back of the pages.
Please show enough (neat) work in the clear spaces left for each prob
Electrical and Computer Engineering Department
Linear System Analysis, ECE531 (Spring 2011)
Final
Friday, May 6, 2011
ame:
You have two hours.
Please do preliminary calculations in the back of the pages.
Please show enough (neat) work in the clear spaces
Illinois Institute of Technology
ECE Department
Linear System Theory, ECE531 (Spring 2013)
Problem Set 1
Issued: Thursday January 17, 2013
Due: Thursday January 24, 2013
Reading Assignment: from your textbook read Chapters One, Two and Three.
Do the follo
Illinois Institute of Technology
ECE Department
Linear System Theory, ECE531 (Spring 2013)
Problem Set 2
Issued: Thursday January 24, 2013
Due: Thursday January 31, 2013
Reading Assignment: Read Chapter Three.
Problems:
Do the following problems from your
Illinois Institute of Technology
ECE Department
Linear System Theory, ECE531 (Spring 2013)
Problem Set 3
Issued: Monday February 04, 2013
Due: Tuesday February 12, 2013
Reading Assignment: Read Chapter Three.
Problems:
Do the following problems from your
Illinois Institute of Technology
ECE Department
Linear System Theory, ECE531 (Spring 2013)
Problem Set 4
Issued: Thursday, February 07, 2013
Due: Thursday, February 14, 2013
Reading Assignment: Read Chapters Three and Four.
Problems:
Do the following prob
ECE 531
LINEAR SYSTEM THEORY
HOMEWORK ASSIGNMENT #2
Due: 14 October 2014
1. Put the matrix
FALL 2014
0 1
0 0
0 0
1 0
A=
0 0
0 1
27 54 36 10
into Jordan form.
2. Let A be a matrix with eigenvalues j1 , j1 , j2 , and j2 , where 1 = 2 .
(a) Show that there
ECE 531
LINEAR SYSTEM THEORY
HOMEWORK ASSIGNMENT #1
Due: 2 October 2014
FALL 2014
1. The following dierential equations represent linear time-invariant systems. Write
down a state space description (state equation and output equation) for each system
in m
ECE 531
LINEAR SYSTEM THEORY
TAKE HOME EXAM #1
Due: 7 November 2014, 5:00 PM (Chicago time)
FALL 2014
This is a take-home exam; open book, open notes. Please list on the exam paper all
outside sources (books, notes, etc.) which you consulted in working th
ECE 531
LINEAR SYSTEM THEORY
TAKE HOME EXAM #2
Due: 11 December 2014, 10:00 AM (Chicago time)
FALL 2014
This is a take-home exam; open book, open notes. Please list on the exam paper all
outside sources (books, notes, etc.) which you consulted in working
SOLUTIONS
Linear System Theory
Assignment #5
Key solutions for the assignments
Hiva Nasiri
[email protected]
32
Eigenvalues: 0, 0
No solution for C1
1
For any m1, [
]
3 1
33
A: not positive, nor semi
B: not positive, nor semi
C: semidefinitive.
34
6,
ANSWERS
Linear System Theory
Assignment #11
Key solutions for the assignments
8.1 Given
2 1
1
() = [
] () + [ ] ().
1 1
2
() = [1 1]()
Find the state feedback gain k so that the state feedback system has -1 and -2 as its eigenvalues. Compute
k directly w
ANSWERS
Linear System Theory
Assignment #10
Key solutions for the assignments
7.1
2 1 2
1
Based on 7.1 and as in 7.8: = [ 1 0 0] , = [0] , = [0
0 1 0
0
1 2], = 0
According to Theorem 7.1 It is not observable (N(s) and D(s) are not coprime)
7.2
2 1
Based o
Electrical and Computer Engineering Department
Linear System Analysis, ECE531 (Spring 2011)
Midterm
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Wednesday, March 9, 2011
Name:
You have one hour fifteen minutes.
Please show enough (neat)
SOLUTIONS
Linear System Theory
Assignment #1
Key solutions for the assignments
Hiva Nasiri
[email protected]
2-3
Linear: x1+x2 => y1, k1x1+k2x2 => (k1+k2) y1
Time Variant: Depends on two variables
Causal: Only depends on past and current time values