### Optimization and Systems Theory Seminar

Friday, Nov. 12, 1999, 11.00-12.00, Room 3721, Lindstedtsv. 25

**Andrey
Ghulchak**

Department of Automatic Control

Lund Institute of Technology

Lund, Sweden

E-mail: ghulchak@control.lth.se

####
Robust controller design via linear programming

The result concerns the particular case of a linear dependence of the
closed-loop characteristic polynomial on an uncertain parameter. In
this case the convex parameterization of all robustly stabilizing
controllers is obtained. The algorithm proposed is a sequence of the
standard linear programming problems of growing dimension which
approximate the original problem. Then the standard free software
(e.g. PCX package) can be used to solve the problem.
The finite dimensional approximation gives us only the lower bound of
the uncertainty radius. However, using the convex duality arguments
the dual problem to the uncertainty radius optimization is derived. It
has mainly the form of H_1 optimization. It is shown that the dual
problem can be solved in the same linear programming framework as the
primal one. It gives the upper bound of the uncertainty radius. So
running both the primal and dual algorithms one can maximize the bound
with a prespecified accuracy.

Calendar of seminars

*Last update: Ocotber 13, 1999 by
Anders Forsgren,
anders.forsgren@math.kth.se.
*