Optimal and Robust Control

Assigned (compulsory) reading

Chapter 12 in Skogestad (2nd edition) is purely dedicated to linear matrix inequalities (LMI) and their application in control analysis and synthesis.

Recommended (not compulsory) further reading

The topic of linear matrix inequalities and the related semidefinite programming is dealt with in numerous resources, many of them available online. The monograph [1] was perhaps the first systematic treatment of the topic and still offers a relevant material. It is available for a free download on the author's website. The authors also provide some shorter teaching material, tailored to their Matlab toolbox called CVX [3]. Another recommendable resource is the lecture notes [2], also available for free. Finally, a very useful material for studying the topic can be found among the tutorials and examples for Yalmip software [4], which is a Matlab interface to a numerous optimization solvers.

[1] Stephen Boyd, Laurent El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory. Volume 15 of Studies in Applied Mathematics
Society for Industrial and Applied Mathematics (SIAM), 1994. Available at https://web.stanford.edu/~boyd/lmibook/.

[2] Carsten Scherer and Siep Weiland. Lecture notes for MSc Course ‘‘Linear Matrix Inequalities in Control’’. 2015. Available at https://www.imng.uni-stuttgart.de/mst/files/LectureNotes.pdf

[3] S. Boyd. Solving semidefinite programs using cvx. Lecture notes for EE363. Downloadable at http://stanford.edu/class/ee363/notes/lmi-cvx.pdf, alternativaly, the text https://stanford.edu/class/ee363/sessions/s4notes.pdf is even richer by two pages.

[4] J. Lofberg. Semidefinite programming in Yalmip. https://yalmip.github.io/tutorial/semidefiniteprogramming/.