Systems Theory (Winter Semester)

Dr. rer. nat. habil. F. von Haeseler
Room G07-206
0391/6718155

Solvey Maldonado
Room G07-204
0391/6718154

Philipp Rumschinski
Room G07-205
0391/6711311

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

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.

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.

TBA

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