Department of Electrical and Computer Engineering

ECE 334: State Space Systems Analysis

Spring Semester 2009


Instructor: Prof. Dan Cobb
Office: 3621 Engineering Hall
Email: cobb@engr.wisc.edu
Office Hours: 3:45 TR

Text: Fundamentals of Linear State Space Systems, John S. Bay, McGraw-Hill, 1999.
Lecture: 2:30-3:45 TR, 2534 EH
Homework: 1 assignment every 2 weeks
Grading: Exam #1 - 30%, Exam #2 - 30%, Final Exam - 40%

Prerequisites: ECE 330 and (Math 320 or Math 340 or concurrent registration).
You do not need any previous background in control theory (such as ECE 332). ECE 334 is an entry-level course in the Automatic Control  course sequence. (See ECE Undergraduate Program in Automatic Control.) You will, however, need a solid background in linear algebra and matrix theory. Coming into the course, you will be expected to know what a matrix is, how to add and multiply matrices, and how to find determinants and inverses. Other topics in linear algebra will be reviewed, but it will help if you already know about eigenvalues, eigenvectors, and linear independence.

Goals: The course will give you a basic understanding of the state-space methodology for linear system analysis. The second half of the semester will emphasize automatic control techniques for closed-loop stabilization and eigenvalue placement. In contrast to the frequency-domain concepts of ECE 332, the material in ECE 334 focuses on differential equations and linear algebra. The course culminates in the development of the "separation principle" and its implications to feedback control.

Syllabus

Week

Beginning

Pages

Topics

1

Jan 19

3-22

state equations, integrator diagrams

2

Jan 26

515-522

vectors, matrices

3

Feb 2

148-153, 211-215

eigenvalues, matrix exponential

4

Feb 9

229-232

solution of state equations

5

Feb 16

108-114, 155-158

similarity transformation, eigenvectors, diagonalization

6

Feb 23

245-248, 326-330

modal expansion, companion form

7

Mar 2

94-100

subspaces, asymptotic stability

8

Mar 9

232-245, 292-299

stable subspace, phase plane diagrams, BIBO stability

9

Mar 23

311-321

controllability

10

Mar 30

334-339

controllability decomposition, stabilizability

11

Apr 6

311-321

observability, detectability, duality

12

Apr 13

class notes

Kalman decomposition

13

Apr 20

405-412

state feedback, eigenvalue placement, stabilization

14

Apr 27

430-433

observers, output feedback

15

May 4

433-438

separation principle, minimal conditions for stabilization



HOMEWORK
Assignment #1 Solutions
Assignment #2 Solutions
Assignment #3 Solutions
Assignment #4 Solutions
Assignment #5 Solutions
Assignment #6 Solutions
Assignment #7 Solutions
Assignment #8 Solutions

EXAM #1 (Weeks 1-4): Tuesday, February 24, 7:15 PM, 2305 EH
Practice Problems
Solutions

EXAM #2 (Weeks 5-10): Tuesday, April 14, In Class
Practice Problems
Solutions

FINAL EXAM (Cumulative): Thursday, May 14, 10:05 AM - 12:05 PM, 3534 EH
Practice Problems
Solutions