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.