# Abstract:

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 a single-input, single-output (SISO) transfer function (TF) multiplied by the inverse of the adaptive optics plant dc gain. This observation then leads to a general design methodology which only requires the synthesis of a SISO $H_\infty$ controller and multiplication by constant matrices.