Systems Theory and Automatic Control

Systems Theory (Winter Semester)


Dr. rer. nat. habil. F. von Haeseler
Room G07-206


Solvey Maldonado
Room G07-204

Philipp Rumschinski
Room G07-205

Time and Place

Wednesday, 15.00-17.00 G07-208
Friday, 9.00-11.00 G07-208
Tuesday (Consultation hour), 12.00-13.00 G07-205

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 special properties of continuous/discrete linear/nonlinear systems, e.g. stability, observability, controllability, etc.


Engineering mathematics, linear algebra, ordinary differential equations.

Program of the Course

The following topics will be covered

  • Description of dynamical Systems
    • Modelling
    • Classification
  • Structural properties of linear Systems
    • Linear differential/difference equations
    • Solution, stability, and transformation
    • Controllability, observability, normal form
    • Zeros, and relative degree
  • Structural properties of nonlinear Systems
    • Lyapunov stability
    • Relative degree
    • Transformation for nonlinear Systems
    • Normal form, controllability, observability, zero-dynamics
  • Randomness in dynamic Systems
    • Properties of random signal
    • Random signal and LTI Systems
    • Estimation and filtering
    • Wiener filter
    • Kalman filter
The content might be subject to last minute changes.

Exam Information


Reccommended Bibliography

The students can refer to the following books for additional explanations:
  • Discrete Dynamical Systems
    Galor, Oded
    Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2007

  • Introduction to Mathematical Systems Theory : Linear Systems, Identification and Control
    Heij, Christiaan; Ran, André. ; Schagen, Freek
    Basel : Birkhäuser Verlag, 2007

  • Mathematical Systems Theory I : Modelling, State Space Analysis, Stability and Robustness
    Hinrichsen, Diederich; Pritchard, Anthony J.
    Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2005

  • Introduction to mathematical systems theory : a behavioral approach
    Polderman, Jan Willem; Willems, Jan C.
    New York, NY [u.a.] : Springer, 1998

  • Regelungstechnik 1 : Systemtheoretische Grundlagen, Analyse und Entwurf einschleifiger Regelungen : mit 69 Beispielen, 169 Übungsaufgaben sowie einer Einführung in das Programmsystem MATLAB / Jan Lunze
    Lunze, Jan
    Berlin, Heidelberg : Springer-Verlag, 2008

  • Topics in mathematical system theory
    Kalman, Rudolf Emil ; Falb, Peter L. ; Arbib, Michael Anthony
    New York [u.a.] : McGraw-Hill, 1969

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

  • Mathematical control theory : deterministic finite dimensional systems
    Sontag, Eduardo D.
    New York, NY [u.a.] : Springer, 1998

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

  • Regelungstechnik
    Schulz, Gerd
    München [u.a.] : Oldenbourg, 2002

  • Mehrgrößenregelung - digitale Regelungstechnik - Fuzzy-Regelung ; mit 118 Beispielen und 56 Aufgaben mit Lösungen
    Schulz, Gerd
    München [u.a.] : Oldenbourg, 2002