  Discrete-time linear systems with perturbed initial state are considered. A
disturbance that infects the initial state is said to be $\epsilon$-tolerable
if the corresponding output signal is relatively insensitive to their effects.
In this paper, we will define a new set that characterize each gain matrix K
and the associated feedback control law ui=Kxi, this set will be called the
$\epsilon$-capacity of the gain matrix K. The set of all possible gain matrix
that makes the system insensitive to all disturbances is noted $\Phi\cdot$. The
characterization of $\Phi\cdot$ is investigated, and we propose an algorithmic
approach that allows to determine if a control law is belongs to $\Phi\cdot$ or
not. Numerical simulations are given.
