# Institute of Information Engineering, Automation, and Mathematics

Course unit code:
A422D3_4B
Course unit title:
Dynamic Systems
Mode of delivery, planned learning activities and teaching methods:
lecture – 2 hours weekly (on-site method)
seminar – 2 hours weekly (on-site method)
Credits allocated:
4
Recommended semester:
Process Control – bachelor (full-time, attendance method), 2. semester
Level of study:
1.
Prerequisites for registration:
passed Mathematics I (N424M3_4B)
Assesment methods:
There are two written examinations during the semester and there is a final oral examination.
Learning outcomes of the course unit:
In this course, students got to know the basics of systems science and dynamic systems theory. They are able to distinguish properties of dynamic systems, to choose appropriate methods of mathematical representation of dynamic systems and to analyse dynamic systems. Students were introduced to applications of dynamic systems theory and to basic concepts of dynamic systems control.
Course contents:
The course is divided into three main parts. The first part is devoted to the introduction to systems science, the definition of basic concepts, and the mathematical representation of dynamical systems. The second part deals with the properties of dynamical systems that determine their behavior. The last part presents applications of dynamic systems in technical practice and introduces the concept of control of dynamic systems.

1. Definition of a system. Definition of a dynamic system. Definition of a static system. Definitions of inputs, outputs and states of a dynamic system.
2. Mathematical representation of dynamic systems. Types of mathematical models of dynamic systems.
3. State space. Order of a dynamic system.
4. Applications of mathematical representation of dynamic systems.
5. Basic definitions from control of dynamic systems.
6. Linearity, autonomy, causality and time invariance of dynamic systems.
7. Equilibrium state of a dynamic system.
8. Stability of equilibrium state of a dynamic system.
9. Behaviour of a system in the neighbourhood of an equilibrium state.
10. Stability of a dynamic system.
11. Applications of dynamic system properties for monitoring and control of systems.
12. Applications of control of dynamic systems.
Recommended:
• GMITERKO, A. – ŠARGA, P. – HRONCOVÁ, D.: Teória dynamických systémov. Košice, SjF TU, 2010. 301 s. ISBN 978-80-553-0603-2.
• LUENBERGER, D.G.: Introduction to Dynamic Systems: Theory, Models, and Applications, Wiley, New York, 1979. 460 s. ISBN 978-0-471-02594-8
Language of instruction:
Slovak, English
Name of lecturer(s):
R. Paulen (2023/2024 – Winter)
R. Fáber, R. Paulen (2022/2023 – Winter)
R. Paulen (2021/2022 – Winter)
Course supervisor: