SF2842 Geometric Control Theory 7.5 credits

Geometrisk styrteori

  • Education cycle

    Second cycle
  • Main field of study

  • Grading scale

    A, B, C, D, E, FX, F

Course offerings

Spring 19 SAP for Study Abroad Programme (SAP)

  • Periods

    Spring 19 P3 (7.5 credits)

  • Application code


  • Start date


  • End date


  • Language of instruction


  • Campus

    KTH Campus

  • Tutoring time


  • Form of study


  • Number of places

    No limitation

  • Course responsible

    Xiaoming Hu <hu@kth.se>

  • Target group

    Study Abroad Programme

Intended learning outcomes

This is an advanced course in mathematical systems theory. With the geometric control theory in focus, this course deepens and broadens knowledge and introduces new concepts in the subject. The course aims at that the student can use the geometric approach to treat basic control design and analysis problems for both linear systems and some nonlinear systems. The knowledge and skill acquired in this course also help enhance the student's ability for abstracting engineering problems.

The overall goal of the course is that the student understands and appreciates the theory and various tools in the geometric approach to systems and control; in particular the student should be able to use the underlying methodologies in practical applications.

Measurable goals

After having finished the course the student should be able to do the following:

  • Reinterpret basic control properties such as Controllability and Observability for linear systems as the property of certain invariant subspace.
  • Understand the geometric interpretation of transmission zeros and zero dynamics.
  • Compute invariant subspaces and various controlled invariant subspaces.
  • Apply different algorithms to solve control problems such as DDP, non-interacting control, tracking and output regulation.
  • Explain how the steady state output response is shaped by the input signal.
  • Solve some basic control problems for nonlinear systems that do not have a controllable linearized system.

For the highest grade the student should be in addition able to

  • Explain how the above results and methods relate and build on each other.
  • Explain the mathematical foundation and control implication of the results and algorithms studied in the course.
  • Solve simple but realistic control problems that require the synthesis of different design algorithms.

Course main content

Introduction and motivation, Invariance and controlled invariance, Zeros, Zero dynamics and system inversion, Tracking and non-interacting control, Disturbance decoupling, Internal model principle, Spectral factorization, Nonlinear systems, Geometric control of robotic systems.


In general:

150 university credits (hp) including 28 hp in Mathematics, 6 hp in Mathematical Statistics and 6 hp in Control Theory. Documented proficiency in English corresponding to English B.

More precisely for KTH students:

Passed courses in calculus, linear algebra, differential equations, mathematical statistics, numerical analysis, control theory. A passed course in mathematical systems theory (SF2832) is an advantage.


Geometric Control Theory, lecture notes by Hu and Lindquist.


  • TENA - Examination, 7.5, grading scale: A, B, C, D, E, FX, F

Requirements for final grade

Written examination (TENA; 7,5 hp).

Offered by



Xiaoming Hu (hu@kth.se)


Xiaoming Hu <hu@kth.se>

Supplementary information

Not given 10/11.


Course syllabus valid from: Spring 2016.
Examination information valid from: Autumn 2015.