  We consider low-order controller design for large-scale linear time-invariant
dynamical systems with inputs and outputs. Model order reduction is a popular
technique, but controllers designed for reduced-order models may result in
unstable closed-loop plants when applied to the full-order system. We introduce
a new method to design a fixed-order controller by minimizing the $L_\infty$
norm of a reduced-order closed-loop transfer matrix function subject to
stability constraints on the closed-loop systems for both the reduced-order and
the full-order models. Since the optimization objective and the constraints are
all nonsmooth and nonconvex we use a sequential quadratic programming method
based on quasi-Newton updating that is intended for this problem class,
available in the open-source software package GRANSO. Using a publicly
available test set, the controllers obtained by the new method are compared
with those computed by the HIFOO (H-Infinity Fixed-Order Optimization) toolbox
applied to a reduced-order model alone, which frequently fail to stabilize the
closed-loop system for the associated full-order model.
