References

Even when restricted to control systems, the concept of robustness is quite broad and can be approached from many different angles. In our course we are restricting the focus to the approaches formulated in frequency domain. The main reference for this part of the course is the book (Skogestad and Postlethwaite 2005). The concepts and techniques introduced in our lecture are covered in Chapters 7 and 8 (up to 8.5) of the book.

What we typically do not cover in the lecture, but only due to time constraints, is the topic of structured uncertainties and their analysis using structured singular value (SSV, 𝜇). These are treated in the section 8.6 through 8.11 of the book. It is warmly recommended to have a look at it.

Although the book is not freely available online (only the first three pages are downloadable on the authors’ web page), it is available in a decent number of copies in the university library.

Get the second edition of Skogestad’s book

In case you are interested in getting the book in one way or another (perhaps even by purchasing it), make sure you get the second edition published 2005. The book contains some useful snippets of Matlab code and the first edition relies on some ancient version of Matlab toolboxes, which makes it useless these days.

The topic of modeling uncertainty in frequency domain using weighting filters plugged into additive or multiplicative structures is fairly classical now and as such can be found in numerous textbooks on robust control such as (Doyle, Francis, and Tannenbaum 2009), (Zhou, Doyle, and Glover 1995), (Dullerud and Paganini 2000), (Sánchez-Peña and Sznaier 1998). Although these are fine texts, frankly speaking they offer nearly no guidance for applying the highly advanced concepts to practical problems – they mostly focus on building up the theoretical framework. In this regard, Skogestad’s book is truly unique.

There are some newer texts that appear to be a bit more on the application side such as (Lavretsky and Wise 2024), (Yedavalli 2014) or (Gu, Petkov, and Konstantinov 2013), but I am not familiar them, to be honest.

References

Doyle, John C., Bruce A. Francis, and Allen R. Tannenbaum. 2009. Feedback Control Theory. Reprint of the 1990 edition by Macmillan Publishing. Dover Publications. https://www.control.utoronto.ca/people/profs/francis/dft.pdf.

Dullerud, Geir E., and Fernando Paganini. 2000. A Course in Robust Control Theory: A Convex Approach. Texts in Applied Mathematics. New York: Springer-Verlag. https://doi.org/10.1007/978-1-4757-3290-0.

Gu, Da-Wei, Petko H. Petkov, and Mihail M. Konstantinov. 2013. Robust Control Design with MATLAB. 2nd ed. Advanced Textbooks in Control and Signal Processing. New York: Springer. https://doi.org/10.1007/978-1-4471-4682-7.

Lavretsky, Eugene, and Kevin Wise. 2024. Robust and Adaptive Control: With Aerospace Applications. 2nd ed. Advanced Textbooks in Control and Signal Processing (C&SP). Cham: Springer. https://doi.org/10.1007/978-3-031-38314-4.

Sánchez-Peña, Ricardo S., and Mario Sznaier. 1998. Robust Systems Theory and Applications. 1st ed. Wiley-Interscience.

Skogestad, Sigurd, and Ian Postlethwaite. 2005. Multivariable Feedback Control: Analysis and Design. 2nd ed. Wiley. https://folk.ntnu.no/skoge/book/.

Yedavalli, Rama K. 2014. Robust Control of Uncertain Dynamic Systems: A Linear State Space Approach. New York: Springer. https://doi.org/10.1007/978-1-4614-9132-3.

Zhou, Kemin, John C. Doyle, and Keith Glover. 1995. Robust and Optimal Control. 1st ed. Prentice Hall.