(Information updated February 21, 2011)
Course contents
Linear (timevarying and timeinvariant)
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

Examination details

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 Discretetime state space models. Special cases: timeinvariant systems, periodic systems. Internal stability. 
2.12, 3.5, 3.6, 3.15, 4.13, 4.16 
3  4 Jan 24 
Chapters 7, 8, 2224 Lyapunov stability. Additional stability results. Stability for discretetime 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 Discretetime Gramians. Discretetime 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 Inputoutput 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, SmithMcMillan form 
15.1, 15.2, 29.4 
12 
17 April 28 
Additional material Differentialalgebraic 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 