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KTH / Engineering Science / Mathematics / Optimization and Systems Theory

SF2842 Geometric Control Theory

Examiner and lecturer

Xiaoming Hu (hu@math.kth.se), Room 3532, Lindstedtsv. 25, tel. 790 7180.

Teaching assistant

Yuecheng Yang (yuecheng@math.kth.se), Lindstedtsv. 25, tel. 790 7132.

Course registration

Important! pleae read here for information on course registration and exam application.

Course contents

The goal of the course is to give students good knowledge about the fundamental results in the geometric control theory. Here is an introduction to the course.

Course material

Course requirements

The course requirements consist of an obligatory final written examination. There are also three homework sets we strongly encourage you to do. All these optional activities will not only give you bonus credits in the examination, but also help you understand the course material better.


Each homework set consists of not more than five problems. Each successfully completed homework set gives you maximally 5 points for the exam. The exact requirements will be posted on each separate homework set. The homework sets will be posted roughly ten days before the deadline on the course homepage.
Note: The date in parentheses is the last day (before 5 pm) for handing in the written solutions. The homework questions will be made available online about ten days before the deadline.
2015 Homework and solution:

Written exam

Written exam will be compulsory from V16.

This is an open book exam and you may bring the lecture notes, the exercise notes, your own classnotes and Beta Mathematics Handbook (or any equivalent handbook). The exam will consist of five problems that give maximally 100 points. These problems will be similar to those in the homework assignments and the tutorial exercises. The preliminary grade levels are distributed according to the following rule, where the total score is the sum of your exam score and maximally fifteen bonus points from the homework assignments (max credit is 115 points). These grade limits can only be modified to your advantage.

Total credit (points) Grade
>90 A
76-90 B
61-75 C
50-60 D
45-49 E
41-44 FX
The grade FX means that you are allowed to make an appeal, see below.

  • The first exam will take place on March 21, 2016 at 08:00-13:00.
  • Solutions to exam of March 21, 2016 can be found here.


    If your total score (exam score + maximum 15 bonus points from the homework assignments) is in the range 41-44 points then you are allowed to do a complementary examination for grade E. In the complementary examination you will be asked to solve two problems on your own. The solutions should be handed in to the examiner in written form and you must be able to defend your solutions in an oral examination. Contact the examiner no later than three weeks after the final exam if you want to do a complementary exam.

    Course evaluation

    All the students are encouraged to answer the questionnaire on KTH Social.

    Preliminary Schedule for 2016

    F=Lecture, E=Exercise

    Type Day Date Time Hall Topic
    F1.Wed 20/01 13-15 D32 Introduction
    F2.Thu 21/01 10-12 D32 Invariant subspaces
    F3.Fri 22/01 13-15 D41 Invariant subspaces (cont.)
    E1.Mon 25/01 15-17 D32 Linear algebra, invariant subspaces
    F4.Wed 27/01 13-15 D42 Disturbance decoupling
    F5.Thu 28/01 10-12 L21 Disturbance decoupling, and Zeros
    F6.Mon 1/02 15-17 D32 Zeros and zero dynamics (cont.)
    E2.Wed 3/02 13-15 E33 Reachability subspaces, V*-algorithm, zero dynamics
    F7.Thu 4/02 10-12 E53 Zero dynamics and high gain control
    F8.Mon 8/02 15-17 E53 Noninteracting control and tracking
    F9.Wed 10/02 13-15 D42 Input-output behavior
    E3. Thu 11/02 10-12 L22 Applications of zero dynamics
    F10.Mon 15/02 15-17 E53 Input-output behavior and Output regulation
    F11.Wed 17/02 13-15 E53 Output regulation (cont.)
    E4.Thu 18/02 10-12 E53 Sylvester equation, Output tracking input, Output regulation
    F12.Mon 22/02 15-17 E33 Nonlinear systems: examples, math preparation
    F13.Wed 24/02 13-15 D42 Nonlinear systems: controllability, stability
    F14.Thu 25/02 10-12 E53 Nonlinear systems: steady state response
    F15.Mon 29/02 15-17 D32 Center manifold and normal form
    E5.Wed 2/03 13-15 D42 Nonlinear systems
    F16.Thu 3/03 10-12 E53 Nonlinear systems: zero dynamics and applications
    F17.Mon 7/03 15-17 D32 Exact linearization and Consensus problem
    F18.Wed 9/03 13-15 E53 Multi-agent systems
    E6.Thu 10/03 10-12 D32 Nonlinear control and multi-agent systems


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    Last updated: 2016-03-22