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227-0690 Advanced Topics in Control
Robust Control & Convex Optimization
Spring 2014



Lecturers: Roy Smith
Paul Goulart
Alberto Giovanni Busetto ETL K 14.1 044 632 46 88 alberto.busetto(at)
Angelos Georghiou ETL K 12 044 632 85 31 angelosg(at)
Marius Schmitt ETL K 12 044 632 4274 schmittm(at)


Lecture: Tuesdays 16:15 to 18:00 CAB G 61
Exercises: Fridays 10:15 to 12:00 ETZ D 61.1


Control systems (227-0216-00L), Linear system theory (227-0225-00L), or equivalents, as well as sufficient mathematical maturity.


An optimization based approach to robust control theory and applications. Topics will include: H-infinity and H-2 control design; structured-singular value analysis and synthesis; model reduction; convex optimization; semi-definite programming; and interior point methods.


The majority of the course grade will depend on a written project report. Details of the project will be made available during the course. The idea is that students will choose a robust control design and analysis application; design robust controllers; assess their performance; simulate their behaviour; and write up the results. The relative weighting of the course components in the assessment of the final grade will be:
Exercises: 30 %
Final project proposal: 10 %
Final project report: 60 %


Lecture Date Topic MATLAB code Last revised
01 19.02.2014 Introduction and overview 17.02.2014
02 25.02.2014 SISO robustness analysis 04.03.2014
03 04.03.2014 MIMO robustness analysis 04.03.2014
04 11.03.2014 Stability and Performance 11.03.2014
05 18.03.2014 Convex Optimization 18.03.2014
06 25.03.2014 Duality at KKT Conditions 25.03.2014
07 01.04.2014 Structured singular value I 01.04.2014
08 08.04.2014 Structured singular value II 08.04.2014
09 15.04.2014 Robust synthesis D-K iteration example 15.04.2014
10 29.04.2014 H2 synthesis 29.04.2014
11 06.05.2014 IQCs and Multiobjective Design 06.05.2014
12 13.05.2014 -Synthesis and other problems Aeroelasticity design example 13.05.2014
13 20.05.2014 Model Reduction 20.05.2014
14 27.05.2014 Modeling and validation 27.05.2014

Podcasts of the lectures can be downloaded or viewed online. (2014 lectures, 2012 lectures).


Exercise Date Questions Hints Solutions Last revised
1 21.02.2014 Exercise 1 Solutions 1 21.02.2014
2 28.02.2014 Exercise 2 Solutions 2 27.02.2014
3 07.03.2014 Exercise 3 Solutions 3 07.03.2014
4 14.03.2014 Exercise 4 Hints 4 Solutions 4 14.03.2014
5 21.03.2014 Exercise 5 Solutions 5 21.03.2014
6 27.03.2014 Exercise 6 Solutions 6 27.03.2014
7 04.04.2014 Exercise 7 Solutions 7 04.04.2014
8 11.04.2014 Exercise 8 Solutions 8 08.05.2014
9 2.05.2014 Exercise 9 2.05.2014
10 8.05.2014 Exercise 10 8.05.2014
11 15.05.2014 Exercise 11 15.05.2014

Grades for each exercise can be found here.

Exercises will be distributed each week in the exercise session, and made available here for download. The assistants will present background material for the exercise in the exercise session and be available to answer questions.

We expect to assign 10 exercises for the class. The grading will be on a quantized scale: 0, 1 or 2. However only your best 8 exercise scores will count towards your course grade.

Exercises must be done individually. You are encouraged to discuss the exercises amongst yourselves but are not allowed to share your solutions or other written material.

The email address for submissions is Exercises should be handed in as PDF attachments to an email to this address, with filename ATICXX-Surname-StudentNumber.pdf, where XX is the exercise number. For example ATIC01-Jones-01-234-567.pdf. The exercises must be submitted no later than 09.59 on the next Friday. The assistants will discuss the solution during the exercise session immediately following the deadline.


The office will be on Wednesdays at 4-5pm in ETL I10. During the office hours you can ask questions about the homework and your individual projects.


The details of the design project are given in the attached description (updated: 16 April 2014).

For examples of prior student projects, please see here. You may use any of the models given in these earlier projects as the starting point for your own project.

Date Project submission Filename for submission
18.04.2014 1 page preliminary proposal ATICprop-Surname-StudentNumber.pdf
01.06.2014 5 page project report ATICreport-Surname-StudentNumber.pdf

The email address for the submission of these items is The proposal and report must be handed in as PDF attachments to an email to this address, with filename given in the above table.

The preferred software for creating both the proposal and the report is LaTeX or one of its variants (MikTeX, Texshop, etc.). The following .cls and example files can be used to format your report. They are actually those required by almost all IEEE conferences for the submission of papers. Also attached here is an example layout and extensive documentation of paper formatting.

File Description
IEEEtran.cls Class file for IEEEtran style
bare_conf.tex Simple example of a conference paper submission
IEEEtran_HOWTO.pdf Detailed description for using the class file (read only the first parts)

Microsoft Word is not a high quality typesetting program and for most conferences is not acceptable. If you don't know how to use LaTeX and would like to use Microsoft Word instead please make sure all of the following conditions are satisfied:

  • You can make Word generate the correct two-column format with the appropriate font size.
  • The resulting PDF has all fonts embedded and no bitmapped fonts.
  • You are unlikely to want to write another technical paper or report in your career.


The following papers contain details about the material presented in the course.

Authors Year Title and source
Desoer and Wang 1980 "On the Generalized Nyquist Stability Criterion," IEEE Trans. Automatic Control., Vol. 25, No. 2, pp. 187-196.
Doyle 1982 "Analysis of feedback systems with structured uncertainties" IEE Proceedings, Vol. 129, Pt. D, pp. 242-250.
Packard and Doyle 1993 "The Complex Structured Singular Value" Automatica, Vol. 29, No. 1, pp. 71-109.
Scherer, Gahinet and Chilali 1997 "Multiobjective Output-Feedback Control via LMI Optimization" IEEE Trans. Automatic Control, Vol. 42, No. 7, pp. 896-911.
de Oliveira, Geromel and Bernussou 2002 "Extended H_2 and H_infinity norm characterizations and controller parametrizations for discrete-time systems," Int. J. Control, Vol. 75, No. 9, pp. 666-679.
Laughlin, Jordan and Morari 1986 "Internal model control and process uncertainty; mapping uncertainty regions for SISO controller design," Int. J. Control, Vol. 44, No. 6, pp. 1675-1698.