ECE 1659H: Robust and Optimal Control

This is the public-facing website for the University of Toronto course ECE1659H "Robust and Optimal Control". This website is unofficial and for informational purposes only. Enrolled students should consult the course website hosted on Quercus for the official course information sheet.

Course Information

Calendar 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.

Course Notes

  • 1x1 format (pdf)

  • 2x1 format (pdf)

Supplementary References

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)