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SF2832 Mathematical Systems Theory 7.5 credits

Choose semester and course offering to see current information and more about the course, such as course syllabus, study period, and application information.

Headings with content from the Course syllabus SF2832 (Autumn 2022–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

  • Linear systems
  • Systems of linear differential equations
  • Controllability and observability
  • Stability
  • Minimality and realization
  • Feedback, pole placement and observer
  • Linear quadratic control, Riccati equations
  • Kalman filters.

Intended learning outcomes

To pass the course, the student shall be able to

  • Analyze linear systems with respect to stability, minimality, observability, and reachability.
  • Use design methods for state feedback and optimal filtering, and analyze properties of the closed loop system.
  • Apply the methods given in the course to solve example problems and use Matlab to solve realistic problems numerically.

To receive the highest grade, the student should in addition be able to

  • Combine and explain the tools in the course and apply them to more complex problems.

Literature and preparations

Specific prerequisites

  • English B / English 6
  • Completed basic course in mathematical statistics (SF1914, SF1918, SF1922 or equivalent)
  • Completed basic course in numerical analysis (SF1544, SF1545 or equivalent)
  • Completed basic course in differential equations (SF1633, SF1683 or equivalent).

Recommended prerequisites

A completed course in control theory.


No information inserted


Lindquist & Sand: An introduction to mathematical systems theory.

Material from the department of Mathematics.

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

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


  • HEM2 - Homework, 1.5 credits, grading scale: P, F
  • TEN2 - Written exam, 6.0 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted


Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

Main field of study


Education cycle

Second cycle

Add-on studies

SF2852 Geometric control theory.


Xiaoming Hu (