In this paper we first present a full order $H_{\infty }$ controller for a multi- input, multi-output (MIMO) adaptive optics system. We apply model reduction techniques to the full order $H_{\infty }$ controller and demonstrate that the closed-loop (CL) system with the reduced order $H_{\infty }$ controller achieves the same high level of performance. Upon closer examination of the structure of the reduced order $H_{\infty }$ controller it is found that the dynamical behavior of the reduced order $H_{\infty }$ controller can be accurately approximated by...