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dc.contributor.authorCastagnotto, Aen_US
dc.contributor.authorGugercin, Sen_US
dc.contributor.authorBeattieen_US
dc.date.accessioned2017-01-26T22:59:42Z
dc.date.available2017-01-26T22:59:42Z
dc.date.issued2016-08-01en_US
dc.identifier.urihttp://hdl.handle.net/10919/74436
dc.description.abstractWe 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.publisherSpringeren_US
dc.relation.ispartofModel Reduction of Parametrized Systems IIIen_US
dc.relation.ispartofseriesModeling, Simulation & Applications (MS&A) Seriesen_US
dc.relation.urihttp://arxiv.org/abs/1610.01039v1en_US
dc.subjectmath.NAen_US
dc.subjectmath.NAen_US
dc.subjectcs.NAen_US
dc.subjectmath.DSen_US
dc.titleInterpolatory methods for $\mathcal{H}_\infty$ model reduction of multi-input/multi-output systemsen_US
dc.typeBook chapter
dc.description.versionAccepted (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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