Seminar Details
2008-10-14 (14.00) : "Plane geometry and convexity of polynomial stability regions"
At Euler
Organized by Mathematical Engineering
Speaker :
Didier HENRION (LAAS-CNRS, University of Toulouse, France, and Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic )
Abstract :
The set of controllers stabilizing a linear system is generally non-convex in the parameter space. In the case of two-parameter controller design (e.g. PI control or static output feedback with one input and two outputs), we observe however that quite often for benchmark problem instances, the set of stabilizing controllers seems to be convex. In this note we use elementary techniques from real algebraic geometry (resultants and B´ezoutian matrices) to explain this phenomenon. As a byproduct, we derive a convex linear matrix inequality (LMI) formulation of two-parameter fixed-order controller design problem, when possible.