Theory of Dynamic Systems

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Control Engineering

Synopsis:

System Approach. Object, System, Model. Dynamic Systems Continuous and Discrete Time, Qualitative Analysis of Systems. Poincare Map, Chaos. Linear Systems. System Stability, Uncertainty and Robustness. Controllability and Observability. State Feedback, State Injection, Duality. Stochastic Systems, Realization of Stochastic Processes.

Requirements:

Basic knowledge of Linear algebra, Basic knowledge of control theory.

Syllabus of lectures:

1. System Theory and Cybernetics, Object, Model, System

2. Linear and Nonlinear Continuous Time Systems

3. Linear and Nonlinear Discrete Time Systems

4. Qualitative Properties of Nonlinear Systems, Bifurcation and Chaos

5. Realization of SISO Systems

6. Composite Systems

7. Stability and Robustness

8. Reachability and Observability

9. Decomposition and Realization, Order Reduction

10. State Feedback

11. State Observers. Separation Principle

12. Output Feedback

13. Uncertainty and its Descriptrion. Stochastic Systems

14. Properties of Output Stochastic Signal. Realization Theorem

Syllabus of tutorials:

The aim of the laboratories is to explain theory presented by the lectures and to solve given problem using MATLAB.

1. Introduction and Repetition

2. Dynamical Properties of Continuous and Discrete Time Systems

3. Examples of Economic, Ecologic and Technical Systems

4. Qualitative Analysis of Nonlinear Systems

5. Discrete Time Systems. Chaotical Behavior of Systems

6. Linear Systems, Linearization, Realization

7. Composite Systems

8. Criterions of Stability, Robust Stability Criterion

9. Criterions of Controllability and Observability

10. System Order Reduction,

11. Examples how to Change Dynamic Properties of System

12. State Observer Design

13. Analysis of Stochastic Systems

14. Realization of Random Signals

Study Objective:

Study materials:

[1] Kailath, T.: Linear Systems. Prentice Hall, Englewood Cliffs, New York,

1980

[2] Antsaklis, P.J., Michel, A.N.: Linear Systems. The McGraw-Hill Co., 1997

Note:

Further information:

https://moodle.dce.fel.cvut.cz/course/view.php?id=46

No time-table has been prepared for this course

The course is a part of the following study plans:

• Erasmus Mundus Master Course - SpaceMaster II (compulsory course in the program)