Robust game theoretic synthesis in the presence of uncertain initial states

In this paper a performance robust control synthesis problem is considered; the performance measure v 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 v 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 v 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.

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