Controller reduction by H∞-balanced truncation

H_∞-balanced truncation may be used to obtain reduced-order plants or controllers. The plant (possibly unstable) is compensated using a particular robustly stabilizing controller. The two Riccati equations involved are then used to define a set of closed-loop input-output invariants called the H_∞-characteristic values. That part of the plant or controller corresponding to small H_∞-characteristic values is discarded to give a reduced-order plant or controller. By exploiting an intimate connection with coprime factorization, a simple a priori test is derived for the ability of such a reduced-order controller to stabilize the full-order plant. The performance of the resulting closed-loop may also be bounded a priori, i.e. in terms of the prespecified level of robustness and the discarded H_∞-characteristic values