ECE 521- MODERN SYSTEMS THEORY

 

Class Time- Spring 2004

4:30-7:10 PM Monday

 

 

Catalog Data: ECE 521- Modern Systems Theory    Prerequisites ECE 320 or equivalent. Introduction to linear systems theory. Review of linear algebra. State variables. State space description of dynamic systems. Analysis of continuous-time and discrete-time linear systems. Controllability and observability of linear systems. Nonlinear systems. Stability theory. Control design.

 

Textbook: W. L. Brogan, Modern Control Theory, Prentice Hall, Third Edition

 

Instructor: Gerald Cook, Earle C. Williams Professor of Electrical and Computer Engineering, (703) 993-1699, Email: gcook@gmu.edu.

 

Office Hours: Monday, 2:30-4:30 and Thursday, 2:30-4:30 or by appointment

 

Goals: This course is designed to introduce advanced undergraduate and beginning graduate students to the fundamental state space concepts needed for the analysis and design of linear systems. The emphasis is on feedback control systems.

 

Prerequisites:

 

1.Signals and systems background

2. Linear algebra

3. Ordinary differential equations

 

Topics:

 

1. State Variables and the State Space Description of Dynamic systems

2. Fundamentals of Matrix Algebra

3. Vectors and Linear Vector Spaces

4. Simultaneous Linear Equations

5. Eigenvalues and Eigenvectors

6. Functions of Square Matrices and the Cayley-Hamilton Theorem

7. Analysis of Continuous- and Discrete-Time Linear State Equations

8. Stability Theory

9. Controllability and Observability for Linear Systems

10. Relationship between State-Variable and Transfer-Function Models

11. Design of Linear Feedback Control Systems

12. Introduction to Optimal Control

 

Grading: Homework-15%   Test1- 25%   Test2- 25%   Final Exam/Project-35%

 

 

 

Homework Assignments

 

1.    3.19, 3.20, 3.21, 3.22, 3.26, 3.27

2.    4.37, 4.40, 4.44, 5.39, 5.47, 5.49

3.    6.30, 6.31, 6.33, 6.34, 6.40, 6.41, 6.42

4.    7.39, 7.40, 7.41, 7.42, 7.48

5.    8.25, 8.27, 8.28, 8.32

6.    9.29, 9.30, 9.31, 9.34, 9.35  Test I during 6th class meeting(March 1st)

7.    9.36, 9.37, 9.40, 9.41  

8.    Lyapunov Stability Problem (to be assigned)

9.    11.27, 11.29, 11.30, 11.34, 11.35, 11.36

10.  12.24, 12.26, 12.28

11.  13.22, 13.23, 13.24, 13.25  Test II during 11th class meeting(April 12th)

12.  13.28, 13.29, 13.30, 13.31, 13.32

13.  Solve via Matlab 14.25, 14.29, 14.31, 14.32

14.    No Homework

 

Final Exam  May 10th  4:30-7:15 PM    Students must be present to take the exam no later than 15 minutes after the scheduled start time.