Optimal filtering techniques for the adaptive optics system of the LBT

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${}_{\mathrm{\infty }}$ 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${}_{\mathrm{\infty }}$ filter and on its advantages and disadvantages over the Kalman filter.