Graduate course on Linear systems, 8p, spring 2007

(Information updated April 10, 2007)
 
Course contents
Linear (time-varying and time-invariant) state space models in continuous and discrete time. Different types of stability. Controllability and observability. Minimal realizations. Balanced realizations. Controller and observer forms. Linear feedback. State reconstruction. Polynomial fraction descriptions. Orientation about extensions.
Prerequisites
The course should be of interest for graduate students in automatic control, signal processing, systems theory, mathematics, mathematical statistics, etc. The participants are assumed to have a basic knowledge of linear dynamic systems and linear algebra.

Structure
The graduate course will be given spring semester 2007. There will be one four hour session per week. Each session will comprise a 2 hour lecture (partly of survey character), and a 2 hour part where the participants will demonstrate solutions to the homework assignments.
Venue and time
The sessions will all take place in room 2344, house 2, Polacksbacken, Uppsala. All meetings will be on Wednesdays, 8.30-12. The first session takes place January 24, 2007.


Literature
  • Wilson J. Rugh: Linear System Theory, second edition. Prentice Hall, 1996.
  • Additional material will be handed out.

Examination details
  • The examination is based on both homework assignments, and a final take-home exam.
  • The participants' solutions to the homework assignments are to be presented and discussed during the problem solving sessions. These sessions are therefore an essential part of the course, and are also aimed to be helpful for the understanding of the material.
  • The take-home exam will be for a period of 4 days, starting May 07.
  • There are no grades (except pass and fail), as for any other PhD course.
  • To pass, a satisfactory performance of both the homework assignments (including presentations at the problem solving sessions) and the final exam is required.
The course will give 8 credit points in the graduate program.

Some other literature on Linear systems is listed here

Schedule

 
Pass Week
Date
 Contents
Homework assignments
1 4
Jan 24
 Chapters 2, 3, 4, 5
Linear state space models. Solutions. Transition matrix properties. Periodic systems. Matrix exponential.
 1.9, 1.17, 1.18,
21.11, 21.12
2 5
Jan 31
 Chapters 20, 21, 6
Discrete-time state space models. Special cases: time-invariant systems, periodic systems.  Internal stability.
 2.12, 3.5, 3.6, 3.15,
4.13, 4.16
3 6
Feb 7
 Chapters  7, 8, 22-24
Lyapunov stability. Additional stability results. Stability for discrete-time systems.
 5.2, 5.14,
20.13, 21.5, 21.8,
6.3, 6.13
4 7
Feb 14
 Chapters 9, 25
Controllability, observability, reachability.
 7.3, 7.5, 7.15,
22.6(j=1), 23.9, 24.1
5 8
Feb 21
 Chapters 10, 11
Realizability. Minimal realizations.
 9.1, 9.4, 9.8,
25.9
6 9
Feb 28
 Chapters 26
Discrete-time Gramians. Discrete-time realizations.
 10.1, 10.8, 10.12,
11.4, 11.12
7 10
March 7
 Additional material
Balanced realizations. Hankel singular values.
 26.4, 26.5, 26.12
8 11
March 14
 Chapters 12, 27, 13
Input-output stability. Controller and observer form.
 Problems handed out
10 13
March 28
 Chapters 14, 28, 15, 29
State feedback. State observation. Reduced observers.
 12.3, 12.13,
13.5, 13.12
11
 14
April 4
 Chapters 16,
Polynomial fraction decompositions. Polynomial matrices.
 14.1, 14.4, 14.7, 14.8
14
 16
May 2
 Additional material.
Polynomial fraction decompositions, Smith-McMillan form
 15.1, 15.2,
29.4
15
 17
  May 9
 Additional material
Differential-algebraic systems (singular systems).
 16.1, 16.2, 16.3, 16.4, 16.6
16
 18
May 16
(Problem solving session)
 Problems to be handed out
17
 19
May 21-25
Final exam

Last updated: 10 April 2007 by Torsten Söderström