Robust Control

General Information

Instructor: Dr. Alireza KARIMI, MER, ME C2 397, tél: 33841.

Objectives: Control of dynamic systems, so that certain properties remain unchanged under perturbations, is considered. In many cases, the controlled system can be presented as a family of dynamic models with parameters or frequency responses lying within admissible sets. Robust control deals with the problem of stability and performance validation for a family of models. The objective of this course is to give an insight into analysis and design of robust control systems. Although the content of course is focused on the H framework, the other approaches to robust control will also be covered in a tutorial way.

. H2 and H spaces (Hilbert and Hardy spaces, computing H2 and H norms)
. Internal stability, uncertainty and robustness (model uncertainty, small gain Theorem, robust stability and performance)
. Performance specifications and limitations (weighting functions, Bode’s integrals, analytical constraints)
. Linear fractional transformation
. H Control and mu-synthesis (problem formulation, general solutions, structured singular values)
. Model and controller reduction (Hankel norm, balanced model reduction, H controller reduction)
. Tutorial on other approaches (presentation by students and/or the instructor):
1. Parametric approach
2. Positive real control
3. Robust pole placement
4. Quantitative feedback theory
5. Convex optimization using LMIs
6. Etc.

Pedagogical vehicles: Ex-cathedra lectures.

Required prior knowledge: Classical control theory and state-space theory.


1. Essentials of robust control by Kemin Zhou with J. C. Doyle
2. Feedback Control Theory by Doyle, Francis and Tannenbaum
3. Linear Matrix Inequalities in System and Control Theory by S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, SIAM 1994 PDF version.
4. Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press 2004 PDF version.
5. LMIs in Control by C. Scherer and S. Weiland, PDF version.
6. LMI Optimization with Applications in Control, D. Henrion and D. Arzelier, PDF version.