Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-80-18-K-4

Introduction to Systems and Control Theory; Dynamical Systems (4V+2U, 9.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U)
4 V Lecture 6.0 CP 56 h 124 h
2 U Exercise class (in small groups) 3.0 CP 28 h 62 h
(4V+2U) 9.0 CP 84 h 186 h


CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg. SuSe
Level [4] Bachelor (Specialization)
Language [EN] English
Area of study [MAT-TEMA] Industrial Mathematics
Livecycle-State [NORM] Active


The course consists of the two parts [MAT-80-12A-K-4] and [MAT-80-17-K-6].

In each summer semester at least one of the courses [MAT-80-18-K-4] or [MAT-80-19-K-4] is offered.

Possible Study achievement

  • Verification of study performance: proof of successful participation in the exercise classes (ungraded)
    The certificate for the exercises ("Übungsschein") consists of the two (partial) certificates for the exercises in the courses [MAT-80-12A-K-4] and [MAT-80-17-K-6].


Introduction to Systems and Control Theory:

Basic terms and ideas of Systems and Control Theory as well as their applications will be discussed. In particular, the following contents will be covered:

  • representation of time-discrete and continuous linear and non-linear dynamic systems,
  • stability of dynamic systems,
  • accessibility, controllability, observability,
  • feedback rule.

Dynamical Systems:

  • basics: existence and uniqueness,
  • autonomous equations,
  • stability theory,
  • nonlinear systems, local theory, theorem of Hartman-Grobman, non hyperbolic equilibrium points and Lyapunov theory,
  • periodic orbits, Poincaré Bendixon and applications, invariant sets,
  • bifurcation theory,
  • applications.

Competencies / intended learning achievements

The students have studied and understand the basic concepts required for describing dynamic systems as well as mathematical techniques for the analysis of these systems and the design of control systems. Furthermore, they are familiar with the various possible applications resulting from the use of mathematical control theory.

In the part "Dynamical Systems", they have studied methods for qualitative treatment of dynamic systems and are able to apply them. The focus is on the behavior of solutions of ordinary differential equations under the influence of varying parameters in a system. The techniques taught are very useful for the study of nonlinear partial differential equations and control theory as well as for the study of practical problems that are modeled by using differential equations.


Introduction to Systems and Control Theory:

  • E. Zerz: Introduction to Systems and Control Theory,
  • J.W. Polderman, J. Willems,: Introduction to Mathematical Systems Theory,
  • H.W. Knobloch, H. Kwakernaak, Lineare Kontrolltheorie,
  • D. Hinrichsen, A.J. Pritchard, Mathematical Systems Theory I,
  • E.D. Sontag, Mathematical Control Theory.

Dynamical Systems:

  • J.K. Hale, H. Kocak: Dynamics and Bifurcations,
  • H. Heuser: Gewöhnliche Differentialgleichungen,
  • B. Marx, W. Vogt: Dynamische Systeme,
  • J.W. Prüss, M. Wilke: Gewöhnliche Differentialgleichungen und dynamische Systeme.
  • K. Burg, H. Haf, F. Wille, A. Meister: Höhere Mathematik für Ingenieure. Band III: Gewöhnliche Differentialgleichungen, Distributionen, Integraltransformationen.


Further literature will be announced in the lecture; Exercise material is provided.


Registration for the exercise classes via the online administration system URM (

References to Course [MAT-80-18-K-4]

Course-Pool Name
[MAT-80-4V-KPOOL-4] Elective Courses Modelling and Scientific Computing (4V, B.Sc.)
[MAT-80-KPOOL-4] Specialisation Modelling and Scientific Computing (B.Sc.)