H_∞‐optimal controller discretization

A redesign method for discretizing a continuous‐time controller is proposed. The resulting hybrid control system, for example with continuous‐time plant and discrete‐time controller, is stable, and performance including the system's inter‐sampling behaviour 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.