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Model reduction by phase matching

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Abstract

This paper discusses procedures for approximating high-order rational power spectrum matrices and minimum phase stable transfer function matrices by lower-order objects of the same type. The basis of the approximation is to secure closeness of a high-order and low-order minimum phase stable transfer function matrix in phase, and to infer from this, closeness in magnitude. A suitable definition of multivariable phase is needed. Particular cases of the approximation procedure which are already known are cast in a general framework, which is also shown to include relative error approximation. A number of error bounds are given. Extensions to approximation of nonminimum phase transfer function matrices are also provided.

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Authors and Affiliations

  1. Department of Electrical Engineering, Imperial College, Exhibition Road, SW7 2BT, London, England

    Michael Green

  2. Department of Systems Engineering, Research School of Physical Sciences, Australian National University, G.P.O. Box 4, A.C.T., Canberra, 2601, Australia

    Brian D. O. Anderson

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  1. Michael Green
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Green, M., Anderson, B.D.O. Model reduction by phase matching. Math. Control Signal Systems 2, 221–263 (1989). https://doi.org/10.1007/BF02551386

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