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 April 17

Tenth and last class.
Decomposition of the state space into p.d. and p.n.d. parts,
giving partitioned state space equations.
Characterization of minimality of Markovian
state space realizations.
See the "List of changes" for the question about
prop. 8.4.3 that came up during class.
 April 10

Ninth class.
Started presentation of chapter 8.
Markovian representations.
It was shown how the forward and backward
generating processes can be used to derive
state space representations of finite dimensional
Markovian representations.
The relation between forward and backward models
described in dual bases was derived.
Next weeks class will be the last of the course.

5B5715 Linear Stochastic Systems  spring 2007
Linear Stochastic Systems
 A geometric approach to modeling, estimation and identification
Spring 2007
 Information about the course
 Lecturer
 Plan for the classes
 Literature:
latest version (jan 28, 2007)
 Lecture notes: These notes are the ones I use for the lectures and
if they are of some use I make them available here after the classes.

Homework 1. You can hand in the homeworks on march 20, or earlier.
While correcting the homeworks, I found an error in the exercise
on Wiener filters.
Therefore, I wrote this note
wiener
to clarify this issue.

Homework 2. The homeworks are now ready.
This time they are more applied and you will need to use Matlab.
Still, the exercises are only simple applications of the theory,
and the methods used are just for illustrating the theory
in the simplest way, and I do not recommend that you use
these approaches to design any airplane controls.
I recommend the seminar by
Alessandro Chiuso on the 11:th
of May for a view of good use of the theory.

Oral exam. Finish the homeworks and then contact me to
book a date for the exam.
There is a lot of material in the book, so to help you a bit I
wrote down the things I think are most important:
study guide.

Exercises.
Some of these exercises will form the home assignments of the course.
Data files:

y_data.mat for exercise 6.8. Contains the variables:

y  5000 outputs of a simulated eigth order linear model

xgen, ygen  (x,y) data of the logarithm of the spectral density
of the generating model
Read the variables into Matlab by writing
"load y_data". (first download the data file to the current Matlab
directory).

modelmag.m Matlab file that can be used to plot the spectral density
corresponding to a transfer function.

model83.mat for exercise 8.3.

model4.mat for exercise 4 in homework 2.
