  In this paper we will discuss the application of optimal filtering techniques
for the adaptive optics system of the LBT telescope. We have studied the
application of both Kalman and H$_\infty$ filters to estimate the temporal
evolution of the phase perturbations due to the atmospheric turbulence and the
telescope vibrations on tip/tilt modes. We will focus on the H$_\infty$ filter
and on its advantages and disadvantages over the Kalman filter.
