Robust performance: unknown disturbances and known fixed inputs

This paper addresses the robust performance problem when the system under consideration is subjected to norm bounded time-varying uncertainty. Different performance objectives are considered, and computable bounds are obtained for the worst case performance in various norms. In some important cases, it is shown that these bounds are tight, giving simple exact formulas for computing robust performance measures. One of the important features of these formulas is that they enable the direct and exact calculation of a number of worst cast performance measures while avoiding entirely the iterations needed for computing these measures by existing methods that rely on repeated scalings and spectral radius bound evaluations.