$H^infty$Control With Initial Conditions

We consider the problem of
$H^infty$
(uniformly optimal) control with non-zero initial conditions. Quantitative results are derived for examining whether the performance of an
$H^infty$
controller is robust against uncertainty in the initial conditions of both the plant and controller. State-space approach for the construction of the controllers that achieve a certain
$H^infty$
performance bound when the magnitude of the initial condition is known to lie within some maximum singular value bound is also presented.