Introduction to Systems Theory
Dr.rer.nat.habil. Friedrich von Haeseler
M.Sc. Christian Kallies
Time and Place (2 SWS Lecture, 2 SWS Exercises)
The lecture will be given in German.
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.
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".
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
available online and for download at http://www.cds.caltech.edu/~murray/amwiki/Main_Page
Discrete Dynamical Systems
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
Further information about the exercises and the exam will be provided later on during the lectures.