Bilinear Matrix Inequalities
- Department of Control Engineering
The focus is on optimization over linear and bilinear matrix inequalities
(LMIs, BMIs), an extension of linear and nonlinear programming to the cone
of positive semidefinite matrices. Since the 1990s, LMI and BMI methods have
found numerous applications mostly in combinatorial optimization, systems
control and signal processing. The course will cover the following topics:
historical developments of LMIs and BMIs; convex sets that can be
represented with LMIs; LMI relaxations of non-convex polynomial optimization
problems, including BMIs; interior-point and augmented Lagrangian algorithms
for LMI and BMI problems; application of LMI and BMI techniques to several
control problems, such as robustness analysis of linear and nonlinear
systems, design of fixed-order robust controllers with Hinf specifications,
static output feedback, simultaneous stabilization.
- Syllabus of lectures:
- Syllabus of tutorials:
- Study Objective:
- Study materials:
Aharon Ben-Tal, Arkadi Nemirovski: Lectures on Modern Convex Optimization.
SIAM, Philadelphia, 2001.
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans: