Summary: We develop here a computationally effective approach for producing high-quality \(\mathcal{H}_{\infty}\)-approximations to large scale linear dynamical systems having Multiple-Inputs Multiple-Outputs (MIMO). We extend an approach for \(\mathcal{H}_{\infty}\) model reduction introduced by G. Flagg et al. [Syst. Control Lett. 62, No. 7, 567–574 (2013; Zbl 1277.93020)] for the Single-Input Single-Output (SISO) setting, which combined ideas originating in interpolatory \(\mathcal{H}_2\)-optimal model reduction with complex Chebyshev approximation. Retaining this framework, our approach to the MIMO problem has its principal computational cost dominated by (sparse) linear solvers, and so it can remain an effective strategy in many large-scale settings. We are able to avoid computationally demanding \(\mathcal{H}_{\infty}\) norm calculations that are normally required to monitor progress within each optimization cycle through the use of “data-driven” rational approximations that are built upon previously computed function samples. Numerical examples are included that illustrate our approach. We produce high fidelity reduced models having consistently better \(\mathcal{H}_{\infty}\) performance than models produced via balanced truncation; these models often are as good as (and occasionally better than) models produced using optimal Hankel norm approximation as well. In all cases considered, the method described here produces reduced models at far lower cost than is possible with either balanced truncation or optimal Hankel norm approximation.
For the entire collection see [Zbl 1381.65001].