Course Description
Contents
The course provides an introduction to recent developments in the area
of Systems and Control, while at the same time covering the standard
theory. The main objects of study in the course are systems modeled by
linear time-invariant differential equations.
We start with a treatment of the theory of algebraic representation of
dynamical systems using polynomial matrices. The main result is a
complete characterization of all representations of a given system.
Several other representations are introduced along with their
relations. Important examples of such representation are input-output
representations that reveal that some variables are unrestricted by the
equations, and state space representations that visualize the
separation of past and future, also referred to as the Markov property.
Controllability and observability are important system theoretic
concepts. A controllable system has the property that a desired future
behavior can always be obtained, independent of the past behavior,
provided that this future behavior is compatible with the laws of the
system. Observability means that the complete behavior may be
reconstructed from incomplete observations. The theory of
controllability and observability forms one of the highlights of the
course.
Stability can be an important and desirable property of a system.
Stabilization by static or dynamic feedback is one of the key features
of Systems and Control. In the pole placement theorem linear algebraic
methods and the notion of controllability are used in their full
strength. The theorem, loosely speaking, says that in a controllable
system the dynamic behavior can be changed as desired, in terms of
characteristic values, by using appropriate feedback. It forms one of
the most elegant results of the course and indeed of the field of
Systems and Control.
Schedule and organisation
The course lasts two weeks: January 19-23 and 26-30. Each day there is
morning and an afternoon session.
- Monday 19 - Tuesday 27:
- Lecture (45 min)
- Exercise class
- Lecture (45 min)
- Lunch break
- Lecture (45 min)
- Exercise class
- Lecture (45 min)
- Wednesday 28 - Thursday 29
- Project work in small groups
- Friday 30:
- Presentation of project work by the project groups
- Certification and closing event