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Latest News

Here you can find the latest news about the course. Old news are archived at news.
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.