In this paper, an alternative approach to conventional Hinf control is proposed for adaptive optic (AO) systems. In order to account for the dynamics of the deformable mirror (DM), the Kirchhoff plate equation is considered. Phase wavefront aberrations, which are the effect of atmospheric turbulence, are modelled using the orthogonal set of Zernike polynomials. The first part of this study concerns the derivation of mathematical models for the DM and the atmospheric turbulence. The AO systems used for disturbance rejection concentrate on a specific frequency band, as the disturbance occurs in that region. However, the conventional weighted Hinf controller is not applicable due to its order. The proposed controller handles this problem by using frequency weighted balanced model reduction. The efficiency of the proposed approach is examined on Zernike?s tip and tilt, focus, astigmatism, coma, trefoil, spherical, secondary astigmatism and quadrafoil modes.