Theory of Dynamic Systems

Lecturer:

Tutor:

Supervisor:

Department of Control Engineering

Synopsis:

System Approach. Object, System, Model. Dynamic Systems Continuous and Discrete Time, Linear Systems - input-output and state space description. System realization. Composed Systems. Solution of state space equations. Discretization. Sampling synchronous and asynchronous. Controllability and Observability. Stability and robustness. State Feedback, State Injection and observer. Separation principle. Nonlinear systems, bifurcation and chaos. Stochastic Systems, Realization of Stochastic Processes.

Requirements:

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. Realization of SISO and MIMO systems

5. Composite Systems

6. Solution of state space equations, numerical methods. State transition matrix

7. Discretization, sampling

8. Reachability and observability

9. Stability and robustness

10. State Feedback

11. State observers. Separation principle.

12. Output feedback Introduction to algebraic system theory.

13. Nonlinear systems, bifurcation and chaos.

14. Uncertainty and its Description. Stochastic Systems. 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. Linear Systems, Linearization, Realization

5. Composite Systems

6. Diferential equations, numerical methods,

7. Discretization

8. Criterions of Controllability and Observability

9. Criterions of Stability, Robust Stability

10. State feedback and its realization

11. Observer, state injection

12. Examples of nonlinear systems

13. Analysis of Stochastic Systems

14. Realization of Random Signals

Study Objective:

Study materials:

1. T. Kailath: Linear Systems. Prentice Hall, Englewood Cliffs, New York, 1980.

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

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Cybernetics and Measurements - Control Engineering- structured studies (compulsory course)
• Cybernetics and Measurements - Artificial Intelligence- structured studies (compulsory course)
• Cybernetics and Measurements - Measurement and Instrumentation Systems- structured studies (compulsory course)
• Cybernetics and Measurements - Aeronautical Engineering and Control Systems- structured studies (compulsory course)