A MEASURE OF WORST-CASE H-INFINITY PERFORMANCE AND OF LARGEST ACCEPTABLE UNCERTAINTY

The structured singular value (SSV or mu) is known to be an effective tool for assessing robust performance of linear time-invariant models subject to structured uncertainty. Yet all a single mu analysis provides is a bound beta on the uncertainty under which stability as well as H(infinity) performance level of k/beta are guaranteed, where k is preselectable. In this paper. we introduce a related quantity nu which provides answers for the following questions: (i) given beta, determine the smallest alpha with the property that, for any uncertainty bounded by beta, an H(infinity) performance level of alpha is guaranteed; (ii) conversely, given alpha, determined the largest beta with the property that, again, for any uncertainty bounded by beta, an H(infinity) performance level of alpha is guaranteed. Properties of this quantity are established and approaches to its computation are investigated. Both unstructured uncertainty and structured uncertainty are considered.