Model reduction by phase matching

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.