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Before choosing course

Course offering missing for current semester as well as for previous and coming semesters
* Retrieved from Course syllabus FEL3340 (Spring 2019–)

Content and learning outcomes

Course contents

Linear time-invariant systems, state space, truncation, residualization/singular perturbation, projection, Kalman decomposition, norms, Hilbert spaces L2 and H2, H∞ space, POD, SVD, PCA, Schmidt-Mirsky theorem, optimization in Hilbert spaces, reachability and observability Gramians, matrix Lyapunov equations, balanced realizations, error bounds, frequency-weighted model reduction, balanced stochastic truncation,  controller reduction, small-gain theorem, empirical Gramians, Hankel-norm, Nehari theorem, Adamjan-Arov-Krein lemma, optimal Hankel-norm approximation

Intended learning outcomes

After the course, the student should:

·         be able to distinguish between difficult and simple model-reduction problems;

·         have a thorough understanding of Principle Component Analysis (PCA) and Singular Value Decomposition (SVD);

·         understand the interplay between linear operators on Hilbert spaces, controllability, observability, and model reduction;

·         know the theory behind balanced truncation and Hankel-norm approximation;

·         be able to reduce systems while preserving certain system structures, such as interconnection topology;

·         be able to reduce linear feedback controllers while taking the overall system performance into account; and

·         to understand, and be able to contribute to, current research in model order reduction.

Course Disposition

Lectures, exercises, homework problems, special focus lectures or participant conducts a project, 24 h take-home exam

Literature and preparations

Specific prerequisites

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Recommended prerequisites

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Lecture notes, research papers, and part of the books

·         Obinata, G. and Anderson, B.D.O., "Model Reduction for Control System Design", Springer-Verlag, London, 2001.

·         Luenberger, D.G., “Optimization by Vector Space Methods”, Wiley, 1969.

·         Green, M. and Limebeer, D.J.N, “Linear Robust Control”, Dover, 2012.

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, 7,0 hp, betygsskala: 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.

Other requirements for final grade

·         75 % on homework problems

·         50 % on take-home exam

·         Participation in special focus lectures alt. conducts a project

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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Profile picture Henrik Sandberg

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 FEL3340

Offered by

EECS/Decision and Control Systems

Main field of study

No information inserted

Education cycle

Third cycle

Add-on studies

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Henrik Sandberg (

Postgraduate course

Postgraduate courses at EECS/Decision and Control Systems