H∞ optimal controller discretization

A redesign method for discretizing a continuous-time controller is proposed. The resulting hybrid control system, e.g. with continuous-time plant and discrete-time controller, is stable, and performance including the system´s intersampling behavior can be optimized by approximating some chosen reference transfer function of the continuous-time control system. In order to obtain a tractable problem, the continuous-time part of the hybrid system and the reference transfer function are approximated by a discrete-time system with arbitrary fast sampling. After lifting the resulting periodic system, the approximation problem can be formulated as a standard H_∞-problem, which is solved using standard software for H_∞ controller design. As an example, a discrete-time controller was determined for the H_∞-optimal controller of a large space structure designed by M.G. Safonov et al. (1988)