On l_∞ robust stability and performance with l_2 and l_∞ perturbations

摘要

In this paper we will consider systems with linear time-invariant perturbations. We will analyze robust performance in the l_2 and l_∞ settings. The l_2 setting gives rise to the familiar case of structured singular values, and a stability criterion is given by the "small μ" theorem. We show that although the necessary and sufficient criterion of robust stability for the l_∞ case (l_∞ stability with structured (l_∞-gain bounded perturbations) is the same "small μ" criterion, a system with l_2-gain bounded perturbations is never l_∞ stable.