ON L(INFINITY) ROBUST STABILITY AND PERFORMANCE WITH L(2) AND L(INFINITY) PERTURBATIONS

In this paper we will consider systems with linear time-invariant pert urbations, We will analyze robust performance in the l(2) and l(infini ty) settings. The l(2) setting gives rise to the familiar case of stru ctured singular values, and a stability criterion is given by the ''sm all mu'' theorem. We show that although the necessary and sufficient c riterion of robust stability for the l(infinity) case (l(infinity) sta bility with structured l(infinity)-gain bounded perturbations) is the same ''small mu'' criterion, a system with l(2)-gain bounded perturbat ions is never l(infinity) stable.