Course detail

Theory of Dynamic Systems

FEKT-MPC-TDSAcad. year: 2020/2021

Systems theory, systemic approach, cybernetics. I/O and state space approach to the analysis and design of dynamic systems, mutual conversions. Continuous, discrete, linear, non-linear, time invariant and time variant systems. System stability. System decomposition. SISO and MIMO systems. Controllability, reachability, observability, reconstructability and realizability of systems. State observers and state feedback. Deterministic and stochastic systems. Bayesian approach to estimation. Kalman filter.

Learning outcomes of the course unit

After passing the course, the student is able to:
- demonstrate and explain the difference between state space and input output description of the system
- explain the concept of causality, realizability, reachability, controlability, observability and reconstructability of the system
- identify and approximate basic types of dynamic systems and discretize the system
- apply the principles of block algebra and Mason’s gain rule for the evaluation of the system’s transfer function
- design the state observer and state feedback
- explain Bayesian approach to estimation and the principle of Kalman filter


The subject knowledge on the Bachelor´s degree level is requested.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Štecha, J., Havlena, V.:Teorie dynamických systémů. Vydavatelství ČVUT, Praha, 1999. (CS)
Ogata, K.: Modern Control Engineering, Fifth edition. Prentice Hall, 2010, ISBN 10: 0-13-615673-8. (EN)
Blaha, P., Bortlík, P., Veselý, L.: Teorie dynamických systémů - sbírka úloh. Skriptum VUT, 2016. (CS)

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations. Materials for lectures and exercises are available for students from web pages of the course. Students have to write a single project/assignment during the course.

Assesment methods and criteria linked to learning outcomes

Numerical Exercises - Max 15 points.
Individual project - Max. 15 points.
Final Exam - Max. 70 points.

Language of instruction


Work placements

Not applicable.

Course curriculum

1. Dynamic system definition and subdivision.
2. Different types of system description: input-output, transfer function, frequency response, polynomials.
3. State space description, state equations, their solution. Modeling of dynamical systems in MATLAB Simulink.
4. Model realization: serial, parallel, direct programming. Canonical forms.
5. Controllability, reachability, observability, reconstruct-ability of systems.
6. Block algebra. Masons’s gain rule for transfer function computation.
7. State feedback. State observers.
8. Methods of continuous time system discretization.
9. Stability of linear and nonlinear systems, stability of interval polynomials.
10. Multi input multi output systems.
11. Bayesian approach to parameter estimation.
12. Kalman filter.
13. Reserve, recapitulation.


The aim of the course is to introduce general system theory and its application to dynamic systems and systemic approach towards control tasks solution.

Specification of controlled education, way of implementation and compensation for absences

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

Classification of course in study plans

  • Programme MPC-KAM Master's, 1. year of study, winter semester, 7 credits, compulsory

Type of course unit



39 hours, optionally

Teacher / Lecturer

Fundamentals seminar

26 hours, compulsory

Teacher / Lecturer