Introduction to Systems Theory

Lecturer

Dr.rer.nat.habil. Friedrich von Haeseler
Room G07-204
0391/67 58155

Assistents

M.Sc. Christian Kallies
Room G07-207
0391/67 52430

Time and Place (2 SWS Lecture, 2 SWS Exercises)

 Mo. 11:00-13:00 G03-106 Fr. 11:00-13:00 G03-106

The lecture will be given in German.

General Information

Systems theory is an interdisciplinary field of science, which is aimed to analyze and study the nature of complex dynamical systems, e.g. biological, economic, and electrical systems. During the course the basics that allow the study and understanding of dynamical processes will be presented. In particular, attention will be focused on continuous/discrete linear systems, plus further details on stochastic processes and Markov chains.

Program of the Course

The following topics will be covered during the course:

• Introduction to Systems Theory:
• What is a system? What is a signal/noise? How are systems described?
• multiple examples.
• Discrete time systems (finite difference equations):
• Solution of difference equations.
• Properties of discrete systems.
• Continuous time systems (differential equations):
• Solution and properties of continuous systems.
• Sampled systems:
• Relationship betweend continuous and discrete systems.
• The sampling problem.
• Introduction to stochastic processes and Markov chains.

The program is subject to change.

Requirements

Important background for the course is Linear Algebra. A review of the essential knowledge will be presented at the beginning of the exercises. Students are kindly required to review the mathematical concepts of "vector", "matrix", and "linearity".

Literature

The following books are recommended for this lecture:

• Feedback systems : an introduction for scientists and engineers
Åström, Karl Johan; Murray, Richard M.
Princeton, NJ [u.a.] : Princeton Univ. Press, 2008
Chapters 1-4

• Discrete Dynamical Systems
Galor, Oded
Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2007
available in the University Network via SpringerLink

• Introduction to dynamic systems : theory, models, and applications
Luenberger, David G.
New York, NY [u.a.] : Wiley, 1979
Chapters 1-5