Theory of Dynamic Systems

Course guarantor:

Branislav Rehák

Lecturer:

Branislav Rehák

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The course provides an introduction to system theory with emphasis on control theory and understanding of the fundamental concepts of systems and control theory. First, we build up the understanding of the dynamical behavior of systems as well as provide the necessary mathematical background. Internal and external system descriptions are described in detail, including state variable, impulse response and transfer function, polynomial matrix, and fractional representations. Stability, controllability, observability, and realizations are explained with the emphasis always being on fundamental results. State feedback, state estimation, and eigenvalue assignment are discussed in detail. All stabilizing feedback controllers are also parameterized using polynomial and fractional system representations. The emphasis in this primer is on linear time-invariant systems, both continuous and discrete time.

Requirements:

Undergraduate-level differential equations and linear algebra (in the extent of the courses 01DIFR, 01LA1, 01LAA2 held at the FNSPE CTU in Prague).

Syllabus of lectures:

1. Introduction to the general theory of systems (decision, control, control structures, object, model, system).

2. Description of the systems (input-output and state space description of the system, stochastic processes and systems, system coupling).

3. Innner dynamics, input- output constraints (solution of state space equations, modes of the system, response of continuous and discrete time systems, stability, reachability and observability).

4. Modification of dynamic properties of the system (state feedback, state reconstruction, separation principle, decomposition and system realization, system sensitivity analysis).

5. Control (state feedback, feedback control systems).

Syllabus of tutorials:

Study Objective:

Knowledges: Students will emerge with a clear picture of the dynamical behavior of linear systems and their advantages and limitations.

Skills: They will be able to describe the system, analyze its properties (stability, controllability, observability) and apply the system theory to particular examples in physics and engineering.

Study materials:

Key references

[1] P. J. Antsaklis, A. N. Michel: A Linear Systems Primer. Birkhäuser, 2007. ISBN-13: 978-0-8176-4460-4

Recommended references

[1] Mikleš, J. a Fikar, M., Process Modelling, Identification, and Control, Springer Verlag, Berlin, 2007. ISBN-13: 978-3540719694

[2] P. J. Antsaklis and A. N. Michel, Linear Systems, Birkhäuser, Boston, MA, 2006. ISBN-13: 978-0817644345

[3] T. Kailath: Linear systems. Prentice-Hall, Englewood Cliffs, NJ, 1980. ISBN-13: 978-0135369616

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: