ECE1659H: Robust and Optimal Control (Winter 2023)

This is the website for the University of Toronto course ECE1659H "Robust and Optimal Control", Winter 2023.

Course Description

Convex optimization methods based on Linear Matrix Inequalities (LMIs) have dramatically expanded our ability to analyze and design complex multivariable control systems. This course explores material from the broad areas of robust and optimal control, with an emphasis on formulating systems analysis and controller design problems using LMIs. Topics include: historical context of robust control, fundamentals of optimization, linear matrix inequalities and semidefinite programming. Linear systems theory: Lyapunov inequalities, input-output performance criteria for dynamic systems, dissipative dynamical systems, and the generalized plant framework for optimal control. LMI solutions of H2 and H-Infinity state and output feedback control problems. Uncertain systems: linear and nonlinear uncertainty modelling, linear fractional representations, robust stability analysis, robust performance analysis. Introduction to integral quadratic constraints.


Competency in classical control (ECE311/ECE356) and linear systems theory (ECE410/ECE557 or equivalent) is required. Introductory knowledge of nonlinear dynamical systems and convex optimization would be highly beneficial, but is not strictly required.


Please see here for the most up to date scheduling information for in-person lectures.

Course Notes

See here.

Supplementary References

  • G. E. Dullerud and. G. Paganini. A Course in Robust Control Theory: A Convex Approach, Springer, 2000. (url)

  • C. Scherer and S. Weiland. Linear Matrix Inequalities in Control. (url)

  • S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory, SIAM, 1994. (url)

  • G. Duan and H. Yu. LMIs in Control Systems: Analysis, Design and Applications, CRC Press, 2013.

  • L. El Ghaoui and S. Niculescu (Eds). Advances in Linear Matrix Inequality Methods in Control, SIAM, 2000.

  • K. Zhou and J. C. Doyle. Essentials of Robust Control, Prentice-Hall, 1998.

  • S. Skogestad and I. Postlethwaite. Multivariable Feedback Control Analysis and Design, Wiley, 2005.

  • C. Desoer and M. Vidyasagar. Feedback Systems: Input-Output Properties, SIAM, 1975. (url)

  • M. Peet. ASU MAE 598/507 (url)

  • S. Lall. Stanford ENGR 201A (url)

  • C. Scherer and S. Weiland LMIs in Control (url)

  • C. Scherer. Theory of Robust Control (url)


John W. Simpson-Porco
Department of Electrical and Computer Engineering
Email: jwsimpson-at-ece-dot-utoronto-dot-ca

Office Hour

By appointment


We will use Piazza, linked off of Quercus, as an asynchronous forum for questions and discussion. As group discussion and back-and-forth is extremely valuable, all students are highly encouraged to participate, and a percentage of the course grade is allotted for participation in the Piazza. 'Participation’ here is broadly defined as positively contributing towards your learning and academic growth and that of your colleagues, and could include asking questions, answering or attempting to answer questions, typing up or linking to related material of interest, etc.

As the Piazza is intended for discussion of course content, I reserve the right to moderate any posts which stray too far off topic.


Homework 40%
Piazza Participation 10%
Project 50%

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