# Control Theory

### General Information:

- Lecture and tutorial in English
- 2 SWS Lecture, 1 SWS tutorial
- 4 ECTS-Credits
- Written closed-book exam.

This course will study the behaviour and properties of linear control systems by looking at their models expressed in ordinary differential equations. Examples of such behaviour and properties include stability, controllability, and observability. By leveraging those models, the design of state feedback controllers and state observers will be provided.

### Content:

- Vector spaces, vector/matrix theory: eigenvalues/eigenvectors, Jordan canonical form, Cayley-Hamilton theorem, singular value decomposition;
- Mathematical description of systems: existence and uniqueness theorems for ordinary differential equations (ODEs), linear ODEs, matrix exponential, non-homogeneous linear ODEs, state-space representations;
- Analysis of linear systems: stability, Lyapunov equations, controllability, observability;
- Realizations: realization theory, balanced realizations, minimum energy inputs;
- Design of linear systems: state feedback and state observers;

### Textbook:

C. T. Chen. "**Linear System Theory and Design**," Oxford University Press, 4th edition, 2012.

### Lecture notes and exercises:

Available at moodle.