Mathematical Systems and Control Theory


Course Objective

After completion of this course the student

1. has knowledge of the theory of finite dimensional linear systems, in
particular in state space form, including the concepts and
characterizations of observability, controllability, minimality of state
space representations, and can apply this knowledge,

2. can design a dynamic feedback compensator for a give state space
system, as well as a linear quadratic controller,

3. has knowledge of, and can apply several models for stochastic systems
as well as stochastic realization theory and basic results on system

4. can construct a Kalman filter for given data and

5. can apply his/her knowledge of systems and control theory with the
aid of Matlab.

Course Content

Many phenomena are characterized by dynamic behaviour where we are
interested in a certain input/output behaviour. Examples are to be found
in the exact and natural sciences (mechanics, biology, ecology), in
engineering (air- and spacecraft design, mechanical engineering) as well
as in economics and econometrics (macro- economical models, trend and
seasonal influences in demand and supply, production systems). Systems
theory is concerned with modeling, estimation and control of dynamical
phenomena. During the course the following subjects will be treated:
models and representations (linear systems, input-output,
state space, transfer function, stochastic systems, spectrum), control
(stabilisation, feedback, pole placement, dynamic programming, the LQ
problem), and identification and prediction (parameter estimation,
spectral analysis, Kalman- filter, model reduction). Applications are in
the area of optimal control and prediction.

Teaching Methods

There is a lecture of two hours each week. In addition, there is another
session which will be half lecture and half practicum, in which there is
the possibility to ask questions about the compulsary computerpracticum.
The practicum makes use of the Matlab package.

Method of Assessment

There are five sets of exercises, which together count for 40%. The
individual final examination concerns the theory and counts for 60%.
The final examination may be either a written exam or an oral
examination, depending on the size of the group.


Chr. Heij, A.C.M. Ran and F. van Schagen, Introduction to Mathematical
Systems Theory, Birkhauser Verlag.

Target Audience

Bachelor Mathematics Year 3, Master Mathematics, Master Business

Recommended background knowledge

Calculus, linear algebra, probability and statistics corresponding to
the level of the courses given at VU.
Analysis corresponding to the level of the analysis course given to BA
students at VU.
Knowledge of complex analysis and Fourier theory is useful, but not
absolutely necessary.

General Information

Course Code X_400180
Credits 6 EC
Period P4+5
Course Level 400
Language of Tuition English
Faculty Faculty of Science
Course Coordinator prof. dr. A.C.M. Ran
Examiner prof. dr. A.C.M. Ran
Teaching Staff prof. dr. A.C.M. Ran

Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods Seminar, Lecture
Target audiences

This course is also available as: