### Optimization and Systems Theory Seminar

Friday, April 4, 2003, 11.00-12.00, Room 3721, Lindstedtsvägen 25

**Chung-Yao Kao **

Institut Mittag-Leffler

Djursholm, Sweden

E-mail: cykao@alum.mit.edu

####
Efficient computational algorithms for IQC analysis

Issues of robust stability and performance have dominated the field of
systems and control theory because of their practical importance. The
recently developed, Integral Quadratic Constraint (IQC) based analysis
method provides a framework for systematically checking robustness
properties of large complex dynamical systems. In IQC analysis, the
system to be analyzed is represented as a nominal, Linear
Time-Invariant (LTI) subsystem interconnected with a perturbation
term. The perturbation is characterized in terms of IQCs. Checking the
condition for robustness is formulated as solving a particular
infinite dimensional optimization problem.
The conventional way of solving this type of optimization problems is
to transform them into Semi-Definite Programs (SDPs) which are then
solved using interior-point algorithms. The disadvantage of this
approach is that the transformation introduces additional decision
variables. In many situations, these auxiliary decision variables
become the main computational burden, and the conventional method then
becomes very inefficient and time consuming. In this talk, a number of
specialized algorithms for solving optimization problems arising from
IQC analysis are presented. The crucial advantage of these newly
developed algorithms is that no auxiliary decision variables are
introduced. The results of our numerical experiments confirm that
these algorithms can solve a problem arising from IQC analysis much
faster than the conventional approach does.

Calendar of seminars

*Last update: March 10, 2003 by
Anders Forsgren,
anders.forsgren@math.kth.se.
*