In this paper a performance robust control synthesis problem is considered; the performance measure η represents the sensitivity of the output to the nonzero initial state. The problem is to find a controller, out of a prescribed set, that minimizes η such that internal stability and a prescribed level of disturbance attenuation for all real parameter uncertainties in a given set are achieved, The primary motivation for considering this problem is that η can be given a direct physical interpretation in terms of the transient response of a closed-loop system, Linear time-invariant systems with output feedback are considered, , A game theoretic approach is employed to solve the synthesis problem and necessary conditions for optimality are given.
