Feedback Control, 2008


This course takes place every two years, in particular during the academic year 2007-2008. It is an advanced course in control theory for linear systems, and provides a very nice field of application of basic linear algebra. It contains a review of some basic concepts from the theory of finite-dimensional, linear, time-invariant systems like controllability, observability, stabilizability and detectability, and the problem of internal stabilization by measurement feedback. The main subject of the course is the so called geometric approach to the study of several feedback synthesis problems for finite dimensional linear systems in state space form. We treat the problem of disturbance decoupling by state feedback and the associated notion of controlled invariance. Next, we consider conditioned invariant subspaces and the problem of estimating an output of the system on the basis of measurement outputs. By combining the theory developed in the contexts of state feedback and estimation we then arrive at the problem of disturbance decoupling by measurement feedback and its extension that requires internal stability of the closed loop system. This problem is studied using the concept of (C,A,B) pair of subspaces. We also look at the problem of external stabilization by measurement feedback. Finally, if time permits, we shift attention to the problems of tracking and regulation. In these problems it is required to design a feedback controller such that the output of the system tracks (follows) an a priori given time signal. The study of this problem uses some very nice fundamental results on the solvability and universal solvability of linear matrix equations.


As material for this course we use the book `Control Theory for Linear Systems', by H.L. Trentelman, A.A. Stoorvogel and M.L.J. Hautus, Springer Verlag, 2001. Unfortunately, the first edition is sold out, and a second edition is not available. However, copies of the book will be made available in the form of lecture notes that can be obtained with Ineke Kruizinga.


In 2008 we will use a new format for this course. There will be no 'hoorcolleges'. Instead, every participant of the course will give a one hour lecture on part of the textbook. In addition, everybody is expected to study the course material on an individual basis, and will get a take home assignment containing a selected set of exercises from the book (can be downloaded below)
Every week there will be a two-hour 'werkcollege' in which the participants work on the problems of the takehome exam, under the guidance of the docent.
At the end of the course there will be a written final examination (closed book).
The organisation of the course will be explained during the first meeting on Tuesday February 12, 13:15 in room 5118.0149. A second meeting will take place on Wednesday, February 13, 9:15, room 5118.0149. During this second meeting we will make a schedule for the presentations that the participants will give. After the second meeting in week 7, participants are expected to start studying the material of the course, and also to start preparing their presentation. In weeks 7 and 8 only 'werkcolleges' are scheduled, see below. In week 10, on Thursday March 6, the first presentation will be given. There will be one one hour presentation per week, followed by discussion, comments, questions, additional remarks, etc. During the presentations, presence of all participants will be obligatory at all times!


week 7: February 11 - 15, 2008
Tuesday 13:15 - 15:00 First meeting Explanation of organisation.
Wednesday 9:15 - 11:00 Second Meeting Fixing the schedule
Thursday 9:15 - 11:00 Werkcollege H.L. Trentelman
week 8: February 18 - 22, 2008
Tuesday 13:15 - 15:00 Werkcollege H.L. Trentelman
Thursday 9:15 - 11:00 Werkcollege H.L. Trentelman
week 10: March 3 - March 7, 2008
Tuesday 13:15 - 15:00 Werkcollege H.L. Trentelman
Thursday 9:15 - 11:00 Presentaties
week 11: March 10 - 14, 2008
Tuesday 13:15 - 15:00 Werkcollege H.L. Trentelman
Thursday 9:15 - 11 :00 Presentaties
week 12: March 17 - 21, 2008
Tuesday 13:15 - 15:00 Werkcollege H.L. Trentelman
Thursday 9:15 - 11:00 Presentaties
week 13: March 24 - 28, 2008
Tuesday 13:15 - 15:00 Werkcollege H.L. Trentelman
Thursday 9:15 - 11:00 Presentaties
week 14: March 31 - April 4, 2008
Tuesday 13:15 - 15:00 Werkcollege H.L. Trentelman
Thursday 9:15 - 11:00 Presentaties

The Presentation

Every participant will give a one hour presentation on the part of the course material that was assigned to him/her. The student should use the blackboard or/and overhead projector. In the presentation he/she is expected to discuss the material that was assigned to him/her. This means that one should follow the main lines, and be careful not to loose oneself in time consuming details.

Download Takehome Exam

The takehome exam should be handed in on or before Friday April 14 Click here to download the takehome exam
The takehome exam consists of a set of selected problems from the course book. During the 'Werkcolleges' participants can work on these problems. The docent will always be present to provide information, and, in case of difficulties, give a helping hand.

Final Examination

There will be a written final examination. A date will be fixed in the near future.

Course Material

The main material for this course consists of parts of chapters 3,4,5,6,9,10 and 11 of the book. The material for the student presentations is taken from these chapters. However, it is necessary to study chapter 2 (necessary material on linear algebra) as well to be able to do the material from chapters 3,4,5,6, 9, 10 and 11. The exact material is the following:
Chapter 2, sections 2.1 t/m 2.7, 2.9 (material on linear algebra)
Chapter 3, sections 3.1 t/m 3.3, 3.5, 3.7, 3.9 t/m 3.12 (this material was already studied in the course System Theory 1, these sections give a quick review)
Chapter 4, sections 4.1, 4.2 and 4.3. (1 hour), sections 4.4, 4.5, 4.6, 4.7, 4.8
Chapter 5, section 5.1, 5.2, 5.3., Chapter 6, sections 6.1 and 6.2 (1 hour), sections 6.3, 6.4
Chapter 9, sections 9.1, 9.2, 9.3 and 9.4 (1 hour)
Chapter 10, sections 10.1, 10.2, 10.3 (1 hour)
Chapter 10, sections 10.4,10.5, Chapter 11, section 11.2 (1 hour)