dc.contributor.author Castagnotto, A en_US dc.contributor.author Gugercin, S en_US dc.contributor.author Beattie en_US dc.date.accessioned 2017-01-26T22:59:42Z dc.date.available 2017-01-26T22:59:42Z dc.date.issued 2016-08-01 en_US dc.identifier.uri http://hdl.handle.net/10919/74436 dc.description.abstract We develop here a computationally effective approach for producing high-quality $\mathcal{H}_\infty$-approximations to large scale linear dynamical systems having multiple inputs and multiple outputs (MIMO). We extend an approach for $\mathcal{H}_\infty$ model reduction introduced by Flagg, Beattie, and Gugercin 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 solves, 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. en_US dc.publisher Springer en_US dc.relation.ispartof Model Reduction of Parametrized Systems III en_US dc.relation.ispartofseries Modeling, Simulation & Applications (MS&A) Series en_US dc.relation.uri http://arxiv.org/abs/1610.01039v1 en_US dc.subject math.NA en_US dc.subject math.NA en_US dc.subject cs.NA en_US dc.subject math.DS en_US dc.title Interpolatory methods for $\mathcal{H}_\infty$ model reduction of multi-input/multi-output systems en_US dc.type Book chapter dc.description.version Accepted (Publication status) en_US pubs.organisational-group /Virginia Tech pubs.organisational-group /Virginia Tech/All T&R Faculty pubs.organisational-group /Virginia Tech/Science pubs.organisational-group /Virginia Tech/Science/COS T&R Faculty pubs.organisational-group /Virginia Tech/Science/Mathematics
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