The University of Texas at
Austin
Deptartment of Electrical
and Computer Engineering
EE380K: Introduction to System Theory
Fall Semester 2010
Some Basic Information
Instructor:
Constantine Caramanis
Email: caramanis AT mail DOT utexas DOT edu
Phone: (512) 4719269
Office: ENS 426
Office Hours: M: 2:00 pm  3:00 pm. W: 2:00 pm  3:00 pm, and by appointment
Lectures:
 Time: Monday and Wednesday, 12:302:00 PM,
 Location: ENS 127
Course Overview
This class is at once an introduction to Systems Theory, and a class in Advanced Linear Algebra.
The concepts from System Theory, including state and
dynamics, feedback, stability, robustness, and estimation, are
pervasive in many areas of both research and application, well beyond
what is traditionally termed "systems and control." System theoretic
ideas are playing an increasing role in networks and Internet
applications (e.g., congestion control), Communications, Signal
Processing, MDPs, Game Theory,
Robust Optimization, and also Information Theory (feedback
channels, communication constraints, etc.), Hidden Markov Models,
and many others.
The purpose of this class will be to develop the mathematical tools as
well as the concepts and intuition of System Theory, in particular
Linear Dynamical Systems, in order to prepare the students for further
work in a wide variety of areas.
Linear Algebra is foundational in many topics important to CommNetS and beyond. Thus, in addition to introducing linear algebra tools important for our study of concepts from System Theory, we will also introduce many topics, methods, concepts and tools that are more generally important.
Official Course Description
This class gives an
introduction to the basic theory of linear dynamical systems in both
discrete and continuous time, with applications to circuits, signal
processing, communications, and control systems. Applied linear
algebra will be a central part of the class, and the first part of the class will be devoted
to developing important tools from linear algebra, which will then resurface many
times through the rest of the course. Important topics we
will cover include:
Course Outline (tentative):
Linear algebra review.
Least squares, and applications: Solution to overdetermined systems.
Least norm solution to underdetermined systems. Robustness
and regularization.
Symmetric matrices. Eigenvalues and Eigenspaces. Invariant Subspaces.
Invariant subsaces. Jordan Canonical Form, and Singular Value Decomposition.
Matrix norms. Matrix perturbation. Small gain theorem. Total least squares.
Structured singular value. Robust performance measures.
Dynamic Systems. Statespace models. Linearity and Time
Invariance (LTI).
Autonomous Linear Dynamical Systems, Solutions of state space models.
Stability and Lyapunov functions. Positive definite functions and the cone of positive definite matrices.
Reachability/Controllability and Observability. Robust observability and reachability.
An introduction to optimal control. Bellman recursion and the principle of optimality.
LQR and Riccati equations.
There will be a big effort to draw interesting examples
illustrating the basic concepts from a wide area, in order to
give an idea of the applicability and impact ideas from
Systems Theory have had, and are currently continuing to have.
Course Prerequisites
Officially, the listed corequisite for this class is a
course in Real Analysis I, Math 365C, or the equivalent. This
will be quite helpful for what we plan to cover in the class.
A strong background in Linear Algebra is very desirable.
Some basic knowledge of Matlab will also be needed.
General Note: If you are concerned about the prerequisites
or your background, or what the course will cover, please don't
hesitate to contact me by email, or come by
my office hours.
Homework and Exams
In this class there will be roughly weekly
homeworks; there will be two midterm exams in class, and then a final
exam. The weighting will be as follows:
Homework: 15% Midterm Exams: 35% Final Exam: 45%
Class participation: 5%
Policy on Collaboration: Discussion of homework questions is
encouraged. Please be sure to submit your own independent
homework solution. This includes any matlab code required for the assignments.
Late homework assignments will not be accepted.
Text and References
The course will not be taught directly from any lecture notes or text book. The lecture notes written by Mohammed
Dahleh, Munther Dahleh, and George Verghese may be helpful, and these are freely available, courtesy of the authors: they can be
downloaded
here. They are all in a zipfile.
Additional References:
For references on systems theory, see:
Introduction to Dynamic Systems: Theory, Models, and Applications,
by David Luenberger. (A classic in the field).
Linear System Theory and Design, by ChiTsong Chen. (A nice,
wellstructured and easily understandable textbook).
Feedback Control Theory, by Doyle, Francis, and
Tannenbaum. (Also readable, and moreover this book is freely available
online).
A Course in Robust Control Theory, by Dullerud and Paganini. (This
book is more advanced and covers much material that we will not have
a chance to go over. It is a full year treatment of the robustness
we cover towards the middle of the class).
Introduction to Mathematical Systems Theory: A Behavioral
Approach,
by Polderman and Willems. (This book introduces the behavioral viewpoint,
and while more mathematical, it renders certain elements of the theory
quite simple and mathematically elegant).
Robust and Optimal Control, by Zhou, Doyle, and Glover. (This book covers
all the material we see in this class, and goes well beyond it.)
For review of linear algebra, I suggest:
Linear Algebra Done Right, by Sheldon Axler,
Matrix Analysis, by Horn and Johnson,
Topics in Matrix Analysis, by Horn and Johnson.
Lecture schedule (tentative)
Lecture No.  Date  Homework  Solutions  Assigned Reading  Exam

1  Wed Aug 25  problem set 0  solution set 0 
  

2  Mon Aug 30        

3  Wed Sep 1  problem set 1  solution set 1    

HOLIDAY  Mon Sep 6        

4  Wed Sep 8        

5  Mon Sep 13  problem set 2  solution set 2    

6  Wed Sep 15        

7  Mon Sep 20        

8  Wed Sep 22        

9  Mon Sept 27  problem set 3  solution set 3    

10  Wed Sept 29        

11  Mon Oct 4        

12  Wed Oct 6  problem set 4      

MIDTERM #1  Mon Oct 11        midterm 1

13  Wed Oct 13  problem set 5  solution set 5    

14  Mon Oct 18        

15  Wed Oct 20        

16  Mon Oct 25        

17  Wed Oct 27  problem set 6  solution set 6    

18  Mon Nov 1        

19  Wed Nov 3        

20  Mon Nov 8        

21  Wed Nov 10        

22  Mon Nov 15        

MIDTERM #2  Wed Nov 17        Midterm #2

23  Mon Nov 22        

24  Wed Nov 24  problem set 7      

25  Mon Nov 29        

26  Wed Dec 1        

Final Exam  TBA        Final

Homeworks
Homeworks are due Wednesday at the beginning of class.
Early assignments (e.g. Monday in class) are fine, but no late
homeworks will be accepted. You are allowed to drop three (3) homeworks.
You are free to not hand them in, but if you do, we will drop you three
lowest grades.
Homework #0:
Concepts from linear algebra. Vector spaces, linear operators, linearity, range, nullspace.
Homework #1:
More linear algebra. Orthogonality. Rank.
Homework #2:
Matrix norms. Projections. More linear algebra.
Homework #3: SVD. matrix perturbation.
More linear algebra.
Homework #4: Some review for the test.
Homework #5: Some practice with dynamical systems, and notions of stability.
Homework #6: Observability and Reachability, and some review notes on linear state feedback and linear observers.
Homework #7: Optimal control.
Solutions
solution set 0
solution set 1
solution set 2
solution set 3
solution set 5
solution set 6
Announcements
Wed. August 25: Welcome to EE380K. I have posted a tentative lecture, homework, and exam
schedule above. If you have any questions about the class, please feel free to email me, or to
drop by my office (ENS 426) if you prefer.
Questions, Comments, Answers
If you have questions/comments, I encourage you to email me.
I will post questions/comments/answers that might be useful to the entire
class here.