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Autoregressive models of singular spectral matrices.

Brian D O Anderson1, Manfred Deistler, Weitian Chen

  • 1Research School of Information Sciences and Engineering, Australian National University, Canberra, ACT 0200, Australia ; Canberra Research Laboratory, National ICT Australia Ltd., PO Box 8001, Canberra, ACT 2601, Australia.

Automatica : the Journal of IFAC, the International Federation of Automatic Control
|March 14, 2013
PubMed
Summary

This study introduces a canonical form for autoregressive (AR) models of singular spectra. This canonical form minimizes model complexity and parameter count for stable transfer function matrices.

Keywords:
Autoregressive (AR) modelCanonical formMatrix fraction description

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Area of Science:

  • System identification
  • Signal processing
  • Control theory

Background:

  • Autoregressive (AR) models are crucial for analyzing time-series data.
  • Representing these models using stable AR matrix fraction descriptions is essential for stability analysis and controller design.
  • Existing methods may not always yield the most parsimonious models.

Purpose of the Study:

  • To derive a canonical form for autoregressive models of singular spectra.
  • To demonstrate advantageous properties of this canonical form for parsimonious modeling.
  • To establish an upper bound on the number of parameters in the canonical AR model.

Main Methods:

  • Derivation of a canonical form for AR models with stable AR matrix fraction descriptions.
  • Analysis of the transfer function matrix properties, including determinantal zeros.
  • Mathematical proofs to establish the minimality of lag, nesting property, and parameter bounds.

Main Results:

  • The derived canonical AR model has a minimal maximum lag within its equivalence class.
  • The canonical form exhibits a nesting property under specified conditions.
  • An upper bound for the total real parameters is established, showing linear growth with matrix dimensions.

Conclusions:

  • The proposed canonical form offers a more parsimonious representation of singular spectrum AR models.
  • This canonical form simplifies model complexity while preserving essential system dynamics.
  • The findings are valuable for efficient system identification and control applications.