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

Low-Order Control Design using a Reduced-Order Model with a Stability Constraint on the Full-Order Model