On the Hankel-norm approximation of linear stochastic systems

Andrea Gombani; Michele Pavon

doi:10.1016/0167-6911(85)90023-4

On the Hankel-norm approximation of linear stochastic systems

Andrea Gombani, Michele Pavon

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We derive ordering and interlocking properties for the singular values of the block-Hankel matrices corresponding to different spectral factors of a given spectral density matrix. The results are then applied to Hankel-norm approximation of SISO stochastic systems. In particular we show that the minimum phase model may be approximated in Hankel norm by systems of a certain prescribed dimension with better accuracy than any other model with the same output process. We also provide upper bounds on the gain in accuracy obtained by choosing the minimum phase model over some other model.

Original language	English (US)
Pages (from-to)	283-288
Number of pages	6
Journal	Systems and Control Letters
Volume	5
Issue number	5
DOIs	https://doi.org/10.1016/0167-6911(85)90023-4
State	Published - Apr 1985

Keywords

Hankel matrices
Hankel-norm approximation
Linear stochastic systems
Singular values
Spectral factors

ASJC Scopus subject areas

Control and Systems Engineering
General Computer Science
Mechanical Engineering
Electrical and Electronic Engineering

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10.1016/0167-6911(85)90023-4

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AU - Pavon, Michele

PY - 1985/4

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N2 - We derive ordering and interlocking properties for the singular values of the block-Hankel matrices corresponding to different spectral factors of a given spectral density matrix. The results are then applied to Hankel-norm approximation of SISO stochastic systems. In particular we show that the minimum phase model may be approximated in Hankel norm by systems of a certain prescribed dimension with better accuracy than any other model with the same output process. We also provide upper bounds on the gain in accuracy obtained by choosing the minimum phase model over some other model.

AB - We derive ordering and interlocking properties for the singular values of the block-Hankel matrices corresponding to different spectral factors of a given spectral density matrix. The results are then applied to Hankel-norm approximation of SISO stochastic systems. In particular we show that the minimum phase model may be approximated in Hankel norm by systems of a certain prescribed dimension with better accuracy than any other model with the same output process. We also provide upper bounds on the gain in accuracy obtained by choosing the minimum phase model over some other model.

KW - Hankel matrices

KW - Hankel-norm approximation

KW - Linear stochastic systems

KW - Singular values

KW - Spectral factors

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EP - 288

JO - Systems and Control Letters

JF - Systems and Control Letters

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ER -

On the Hankel-norm approximation of linear stochastic systems

Abstract

Keywords

ASJC Scopus subject areas

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