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

# Module MAT-80-18-M-4

## Introduction to Systems and Control Theory & Dynamical Systems (M, 9.0 LP)

## Module Identification

Module Number | Module Name | CP (Effort) |
---|---|---|

MAT-80-18-M-4 | Introduction to Systems and Control Theory & Dynamical Systems | 9.0 CP (270 h) |

## Basedata

CP, Effort | 9.0 CP = 270 h |
---|---|

Position of the semester | 1 Sem. irreg. SuSe |

Level | [4] Bachelor (Specialization) |

Language | [EN] English |

Module Manager | |

Lecturers | |

Area of study | [MAT-TEMA] Industrial Mathematics |

Reference course of study | [MAT-88.105-SG] M.Sc. Mathematics |

Livecycle-State | [NORM] Active |

## Courses

Type/SWS | Course Number | Title | Choice in Module-Part | Presence-Time / Self-Study | 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 |
U-Schein
| - | PL1 | 4.5 | SuSe |

2V+1U | MAT-80-17-K-6 | Dynamical Systems
| P | 42 h | 93 h |
U-Schein
| - | PL1 | 4.5 | irreg. SuSe |

- 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-80-17-K-6]: Title: "Dynamical Systems"; Presence-Time: 42 h; Self-Study: 93 h
- About [MAT-80-17-K-6]:
The study achievement
**"[U-Schein] proof of successful participation in the exercise classes (ungraded)"**must be obtained.

## Examination achievement PL1

- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: each semester
- Examination number: 84265 ("Introduction to Systems and Control Theory; Dynamical Systems")

## Evaluation of grades

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

## Contents

- 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

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.

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. They are able to comprehend and explain the propositions and proofs presented in the lectures. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies.

## Literature

- 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.

- 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.

## Registration

## Requirements for attendance of the module (informal)

#### Modules:

- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-14-11-M-3] Introduction to Numerical Methods (M, 9.0 LP)

#### Courses

## Requirements for attendance of the module (formal)

**None**

## References to Module / Module Number [MAT-80-18-M-4]

Course of Study | Section | Choice/Obligation |
---|---|---|

[MAT-88.105-SG] M.Sc. Mathematics | [Core Modules (non specialised)] Applied Mathematics | [WP] Compulsory Elective |

[MAT-88.118-SG] M.Sc. Industrial Mathematics | [Core Modules (non specialised)] General Mathematics | [WP] Compulsory Elective |

[MAT-88.276-SG] M.Sc. Business Mathematics | [Core Modules (non specialised)] General Mathematics | [WP] Compulsory Elective |

[MAT-88.706-SG] M.Sc. Mathematics International | [Core Modules (non specialised)] Applied Mathematics | [WP] Compulsory Elective |

## Notice