Some recent results in structured robust stability: An overview

Some recent results on robust stability with structured perturbations, using the polynomial framework, are presented in this paper without proof. As background we first describe Kharitonov's theorem and give an interpretation of it as a generalization of the Hermite—Bieler interlacing theorem. The need for a generalization of this result for tackling the control problem is explained, and our new results are then presented. An important generalization of Kharitonov's theorem that solves the box problem in parameter space is described. Some efficient formulae for the l²-stability margin in parameter space are also given. The results are illustrated by examples.