We present a new approach for the control of a deformable mirror (DM), part of a Multi Object Adaptive Optics (MOAO) on-sky demonstrator. The control is based on H∞ synthesis methods, achieving better performance than classical Proportional-Integral methods, while offering other appealing advantages such as an optimized design based on the temporal spectra of the wavefront and vibration rejection capabilities. We describe laboratory results obtained with a 97 actuator Xinetics DM, using a high-resolution Shack-Hartmann wavefront sensor for measuring DM surface. A connection between the turbulence dynamics represented in a Zernike basis and the controller requirements is studied, showing that the controller parameters and structure can be easily optimized for each Zernike mode according to their particular temporal spectra. © 2009 SPIE.