H∞ control of linear systems with nonzero initial conditions

In H_∞ (or uniformly optimal) control problems, it is usually assumed that the system initial conditions are zero. In the present work, the authors formulate an H_∞-like control problem that incorporates uncertainty in initial conditions. This is done by defining a worst-case performance measure. Both finite and infinite horizon problems are considered. Necessary and sufficient conditions are derived for the existence of controllers that yield a closed-loop system for which the above-mentioned performance measure is less than a prespecified value. State-space formulae for the controllers are also presented