Interpolatory H-infinity model reduction

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Date
2013-07-01
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Elsevier Science Bv
Abstract

We introduce an interpolation framework for Η∞ model reduction founded on ideas originating in optimal-Η2 interpolatory model reduction, realization theory, and complex Chebyshev approximation. By employing a Loewner "data-driven" framework within each optimization cycle, large-scale Η∞ norm calculations can be completely avoided. Thus, we are able to formulate a method that remains effective in large-scale settings with the main cost dominated by sparse linear solves. Several numerical examples illustrate that our approach will produce high fidelity reduced models consistently exhibiting better Η∞ performance than those produced by balanced truncation; these models often are as good as (and occasionally better than) those models produced by optimal Hankel norm approximation. In all cases, these reduced models are produced at far lower cost than is possible either with balanced truncation or optimal Hankel norm approximation.

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Keywords
Technology, Automation & Control Systems, Operations Research & Management Science, AUTOMATION & CONTROL SYSTEMS, OPERATIONS RESEARCH & MANAGEMENT SCIENCE, H-2/H-infinity approximation, Interpolation, Loewner matrices, Large-scale systems, HANKEL-NORM APPROXIMATIONS, LARGE-SCALE SYSTEMS, RANK SMITH METHOD, MULTIVARIABLE SYSTEMS, BALANCED TRUNCATION, DESCRIPTOR SYSTEMS, LYAPUNOV EQUATIONS, TIME
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