Welcome to Geometric Linear Control Theory

**Description: **In this course, we will study fundamental concepts related to (finite dimensional) linear time-invariant control system such as controllability, observability and stabilizability. These basic concepts will be introduced via the "geometric approach" meaning that they will be related to various subspaces related to the matrices appearing in the system equations. This approach will enable us to introduce the important notion of (A,B)-invariant subspace (and its dual concept, (C,A)-invariant subspace), which will be used to solve the disturbance decoupling problem (and can be used to solve the problem of tracking and regulation). Moreover, the notion of (A,B)-invariant subspace and (C,A)-invariant subspace also turn out to be instrumental in other synthesis problems like observer design, system invertibility, the minimum phase property, and output stabilizability.

**Prerequisites:**

A basic knowledge of mathematics as obtained through undergraduate engineering studies. Knowledge of control is an advantage but not a prerequisite.

Literature: The course will be based on Chapter 4, 5 and 6 of the book [TSH] and the paper [FW]. As preparation it is expected that the participant acquaint themselves with concepts and results corresponding to the material in Chapter 2 and 3 of [TSH].

[TSH] Control theory for linear systems, by Trentelman, Stoorvogel, and Hautus.

[FW] The internal model principle for linear multivariable regulators, by Francis and Wonham.

The book [TSH] can be downloaded from Prof. dr. Harry L. Trentelman's homepage (http://www.math.rug.nl/trentelman/).

**Organizer:**

**Lecturers: **Associate Professor John Leth, Department of Electronic Systems, Associate Professor Mihaly Petreczky, CNRS Lille, France and Professor Rafael Wisniewski, Department of Electronic Systems

**ECTS:** 2

**Time:** 22. - 24. May 2017

**Place:**

**Zip code: **

**City: **

**Number of seats: **50

**Deadline: **1. May 2017

**Important information concerning PhD courses** We have over some time experienced problems with no-show for both project and general courses. It has now reached a point where we are forced to take action. Therefore, the Doctoral School has decided to introduce a no-show fee of DKK 5,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately three months before start. This can hopefully also provide new students a chance to register for courses during the year. We look forward to your registrations.

- Teacher: John-Josef Leth
- Teacher: Rafal Wisniewski