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FEL3210 Multivariable Control 8.0 credits

The course will give an introduction to the design and analysis of robust linear multivariable control systems. The focus is on inherent limitations in feedback systems and on stability and performance in the presence of uncertainty. Important topics include: signal and system norms, performance specifications and inherent limitations, uncertainty descriptions,  robust stability and robust performance. structured uncertainty and mu, H_infty- and H_2-optimal control, LQG cast as H_2-optimal control, H_infty loop shaping, mu-synthesis, LMIs, gap metrics.

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Headings with content from the Course syllabus FEL3210 (Autumn 2019–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Multivariable frequency response analysis, directionality in MIMO systems (SVD), input-output controllability, uncertainty models, linear fractional transformations, robustness analysis including the structured singular value, mu-synthesis, H2- and H-infty controller synthesis, H-infty loop shaping, Glover-MacFarlane robust loopshaping, control structures including decentralized control, gap metrics, linear matrix inequalities, Integral Quadratic Constraints

Course structure

Lectures and compulsory homeworks, take-home exam

Course literature

Skogestad and Postlethwaite, Multivariable Feedback Control, 2nd Ed., Wiley, 2009
Supplementary: Zhou, Doyle and Glover, Robust and Optimal Control, Prentice Hall, 1996

Intended learning outcomes

After completing the course, the student should be able to:

  • describe and explain the general principles for analysis and synthesis of linear multivariable robust control systems.
  • derive fundamental limitations in feedback systems based on interpolation constraints and analytic constraints on closed-loop transfer-functions
  • model uncertainty in linear dynamic systems using model sets
  • analyze robust stability and robust performance of multivariable feedback systems with respect to structured and unstructured uncertainty
  • quantify the achieveable control performance for a given system
  • design/synthesize multivariable controllers for robust performance
  • contribute to the research front in the main areas covered by the course

Course disposition

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Literature and preparations

Specific prerequisites

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Recommended prerequisites

Undergraduate course in classic SISO control, elementary background in matrices and linear algebra. An introductory course in multivariable control is recommended, but not a requirement.


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Examination and completion

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

Grading scale

P, F


  • EXA1 - Examination, 8.0 credits, grading scale: P, 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.

For passing grade at least 80% score on all homeworks and at least 70% score on exam

Other requirements for final grade

Passing grade on all homeworks and take-home exam

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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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 web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web FEL3210

Offered by

Main field of study

This course does not belong to any Main field of study.

Education cycle

Third cycle

Add-on studies

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Elling W Jacobsen (

Postgraduate course

Postgraduate courses at EECS/Decision and Control Systems