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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

Silun Zhang (silunz@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.
  • Homework 1, Solution (Due February 7, 2017)
  • Homework 2, Solution (Due February 22, 2017)
  • Homework 3, Solution (Due March 8, 2017)
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.
2016 Homework and solution:

Written exam

Written exam has been 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 15, 2017 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 2017

    F=Lecture, E=Exercise

    Type Day Date Time Hall Topic
    F1.Tue 17/01 13-15 D41 Introduction
    F2.Wed 18/01 13-15 E53 Invariant subspaces
    F3.Thu 19/01 10-12 D34 Invariant subspaces (cont.)
    E1.Mon 23/01 15-17 D32 Linear algebra, invariant subspaces
    F4.Tue 24/01 13-15 D32 Disturbance decoupling
    F5.Wed 25/01 13-15 L21 Disturbance decoupling, and Zeros
    F6.Thu 26/01 10-12 E31 Zeros and zero dynamics (cont.)
    E2.Mon 30/01 15-17 D32 Reachability subspaces, V*-algorithm, zero dynamics
    F7.Wed 1/02 10-12 D42 Zero dynamics and high gain control
    F8.Thu 2/02 10-12 D32 Noninteracting control and tracking
    F9.Mon 6/02 15-17 L21 Input-output behavior
    E3. Tue 7/02 13-15 E53 Applications of zero dynamics
    F10.Wed 8/02 13-15 E33 Input-output behavior and Output regulation
    F11.Thu 9/02 10-12 E35 Output regulation (cont.)
    E4.Mon 13/02 15-17 E31 Sylvester equation, Output tracking input, Output regulation
    F12.Wed 15/02 13-15 D41 Nonlinear systems: examples, math preparation
    F13.Thu 16/02 10-12 E31 Nonlinear systems: controllability, stability
    F14.Mon 20/02 15-17 D32 Nonlinear systems: steady state response
    F15.Tue 21/02 13-15 L22 Center manifold and normal form
    E5.Wed 22/02 13-15 D41 Nonlinear systems
    F16.Thu 23/02 10-12 E32 Nonlinear systems: zero dynamics and applications
    F17.Mon 27/02 15-17 D32 Exact linearization and Consensus problem
    F18.Wed 1/03 13-15 D41 Multi-agent systems
    E6.Thu 2/03 10-12 M31 Nonlinear control and multi-agent systems


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    Last updated: 2016-12-30