Computational and Applied Mathematics seminar

Abstract: One of the most fundamental problems in control theory is feedback stability analysis. That is, the problem of determining if two systems interconnected via feedback will be stable. In the case of linear time-invariant systems, under mild conditions the solvability of a set of linear matrix inequalities (LMIs) is a both necessary and sufficient condition for stability. Nevertheless, models of reality are always imperfect, and in robust stability analysis one therefore instead consider the problem if a feedback interconnection between a nominal system and a set of uncertainties is stable for all uncertainties in the set. In this talk, I will present new results on that robustness to certain forms of structured uncertainties is equivalent with the existence of certain forms of structured solutions to the LMIs. The talk is aimed to be self-contained; no prior knowledge on control theory is needed, and all relevant concepts will be introduced and explained.