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Before choosing course

This course aims at introducing some mathematical tools which are essential for understanding fundamental results underlying several areas of automatic control, signal processing and communications. In particular, the course focuses in aspects of functional analysis, specifically related to the basics of Hilbert and Banach spaces. Since the course is mainly targeted at graduate students in Electrical Engineering, the theory is complemented with several examples from areas such as robust control, game theory, model reduction, estimation/filtering theory and system identification.

Course offering missing for current semester as well as for previous and coming semesters
* Retrieved from Course syllabus FEL3370 (Spring 2019–)

Content and learning outcomes

Course contents

Introduction: Inner product spaces; Normed spaces; Hilbert and Banach spaces; Orthogonal expansions; Least squares estimation; Dual spaces; Contraction mappings/ Banach fixed point theorem; Linear operators and adjoints; Optimization of functionals; Application to H infinity control theory.

Intended learning outcomes

After completing this course, the student will be able to follow the derivations and subtleties of a number of results available in publicaitons in Electrical Engineering, and to eventually contribute to the underlying theories of this field.

Course Disposition

  • Lectures
  • Homework exercises
  • Final project (presentation on selected topics by the participants)

Literature and preparations

Specific prerequisites

The course is open to all graduate students. (no prerequisite courses)

Recommended prerequisites

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N.Young. An Introduction to Hilbert Space. Cambridge University Press 1988

Some excellent complements are:

E.Kreyszig. Introductory Functional Analysis with Applications. Wiley 1989

D.G. Luenberger. Optimization by Vector Space Methods. Wiley 1969

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 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

80% on weekly homework exercises and 20% project (analysis of a reserach paper, preferably related to the student´s own research, and a 15 minutes presentation of the main ideas/ results of such paper)

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 Cristian Rojas

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 FEL3370

Offered by

EECS/Decision and Control Systems

Main field of study

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Education cycle

Third cycle

Add-on studies

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Postgraduate course

Postgraduate courses at EECS/Decision and Control Systems