Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-80-12-M-6

Systems and Control Theory (M, 9.0 LP, AUSL)

Module Identification

Module Number Module Name CP (Effort)
MAT-80-12-M-6 Systems and Control Theory 9.0 CP (270 h)


CP, Effort 9.0 CP = 270 h
Position of the semester 2 Sem. from irreg.
Level [6] Master (General)
Language [EN] English
Module Manager
+ further Lecturers of the department Mathematics
Area of study [MAT-TEMA] Industrial Mathematics
Livecycle-State [AUSL] Phase-out period


This module comprises the two modules [MAT-80-12A-M-4] and [MAT-80-12B-M-7].

Without a proof of successful participation in the exercise classes, only 7.5 credit points will be awarded for the module.


Type/SWS Course Number Title Choice in
Presence-Time /
SL SL is
required for exa.
PL CP Sem.
2V+1U MAT-80-12A-K-4
Introduction to Systems and Control Theory
P 42 h 93 h
- PL1 4.5 SuSe
2V+1U MAT-80-12B-K-7
Systems and Control Theory: Advanced Topics
P 42 h 93 h - - PL1 4.5 irreg.
  • About [MAT-80-12A-K-4]: Title: "Introduction to Systems and Control Theory"; Presence-Time: 42 h; Self-Study: 93 h
  • About [MAT-80-12A-K-4]: The study achievement [U-Schein] proof of successful participation in the exercise classes (ungraded) must be obtained.
  • About [MAT-80-12B-K-7]: Title: "Systems and Control Theory: Advanced Topics"; Presence-Time: 42 h; Self-Study: 93 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: irregular (by arrangement)
  • Examination number: 84261 ("Systems and Control Theory")

Evaluation of grades

The grade of the module examination is also the module grade.


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.
This course deals with the more advanced topics in control theory and its applications. In particular, the following topics are covered:
  • extended state space and behaviour theory,
  • control concepts,
  • transfer functions and realisation theory,
  • polynomial system models.

Competencies / intended learning achievements

Upon successful completion of this module, the students know and understand basic and advanced concepts for the description of dynamic systems as well as mathematical techniques for the analysis of these systems and for the design of controllers. Furthermore, they are familiar with the application possibilities resulting from the use of mathematical control theory. They understand the proofs presented in the lecture and are able to reproduce and explain them.

By completing the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies independently or by team work.


  • 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.


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

References to Module / Module Number [MAT-80-12-M-6]

Course of Study Section Choice/Obligation
[MAT-88.105-SG] M.Sc. Mathematics Applied Mathematics [WP] Compulsory Elective
[MAT-88.706-SG] M.Sc. Mathematics International Applied Mathematics [WP] Compulsory Elective