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

We propose a new algorithm for designing low-order controllers for large-scale linear time-invariant (LTI) dynamical systems with input and output. While the high cost of working with large-scale systems can mostly be avoided by first applying model order reduction, this can often result in controllers which fail to stabilize the closed-loop plant of the original full-order system. By considering a modified version of the optimal H∞ controller problem that incorporates both full- and reduced-order model data, our new method ensures stability while remaining efficient. Using a publicly available test set, we find that the controllers obtained by our method outperform those computed by RIFOO (H-Infinity Fixed-Order Optimization) when applied to reduced-order models alone.