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Model reduction by phase matching. (English) Zbl 0685.93045

Summary: 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.

MSC:

93C35 Multivariable systems, multidimensional control systems
15A23 Factorization of matrices
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
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