Graduate course on Linear systems, 12 hp, spring 2011

(Information updated February 21, 2011)
 
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 2011. 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 some Mondays and some Thursdays, 13.15. The first session takes place January 17, 2011. Please note that some prepatory homework assignments are due already at the course start.


Literature
  • Wilson J. Rugh: Linear System Theory, second edition. Prentice Hall, 1996. The book is available at Adlibris and at Amazon.
  • 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 2011.
  • 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 12 credit points (hp) in the graduate program.

Some other literature on Linear systems is listed here

Schedule

 
Pass Week
Date
 Contents
Homework assignments
1 3
Jan 17
 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 3
Jan 20
 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 4
Jan 24
 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 5
Jan 31
 Chapters 9, 25
Controllability, observability, reachability.
 7.3, 7.5, 7.15,
22.6(j=1), 23.9, 24.1
5 6
Feb 7
 Chapters 10, 11
Realizability. Minimal realizations.
 9.1, 9.4, 9.8,
25.9
6 7 
Feb 14
 Chapters 26
Discrete-time Gramians. Discrete-time realizations.
 10.1, 10.8, 10.12,
11.4, 11.12
7 7
Feb 17
 Additional material
Balanced realizations. Hankel singular values.
 26.4, 26.5, 26.12
8 13
March 28
 Chapters 12, 27, 13
Input-output stability. Controller and observer form.
 Problems handed out
9
 14
  April 4
 Chapters 14, 28, 15, 29
State feedback. State observation. Reduced observers.
 12.3, 12.13,
13.5, 13.12
10
 15
April 11
 Chapters 16,
Polynomial fraction decompositions. Polynomial matrices.
 14.1, 14.4, 14.7, 14.8
11
 16
April 18
 Additional material.
Polynomial fraction decompositions, Smith-McMillan form
 15.1, 15.2,
29.4
12
 17
  April 28
 Additional material
Differential-algebraic systems (singular systems).
 16.1, 16.2, 16.3, 16.4, 16.6
13
 18
  May2
(Problem solving session)
 Problems to be handed out
14
 19
May 2
Final exam

Last updated: 21 February 2011 by Torsten Söderström