Balanced truncation of linear time-varying systems

Henrik Sandberg; Anders Rantzer

doi:10.1109/TAC.2003.822862

Balanced truncation of linear time-varying systems

Henrik Sandberg, Anders Rantzer

Department of Automatic Control

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Abstract

In this paper balanced truncation of linear time-varying systems is studied in discrete and continuous time. Based on relatively basic calculations with time-varying Lyapunov equations/inequalities we are able to derive both upper and lower error bounds for the truncated models. These results generalize well-known time-invariant formulas. The case oftime-varying state dimension is considered. Input-output stability of all truncated balanced realizations is also proven. The method is finally successfully applied to a high-order model.

Original language	English
Pages (from-to)	217-229
Journal	IEEE Transactions on Automatic Control
Volume	49
Issue number	2
DOIs	https://doi.org/10.1109/TAC.2003.822862
Publication status	Published - 2004

Subject classification (UKÄ)

Control Engineering

Free keywords

linear timevarying systems
Balanced truncation
error bound
model reduction

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10.1109/TAC.2003.822862

01266776

Cite this

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abstract = "In this paper balanced truncation of linear time-varying systems is studied in discrete and continuous time. Based on relatively basic calculations with time-varying Lyapunov equations/inequalities we are able to derive both upper and lower error bounds for the truncated models. These results generalize well-known time-invariant formulas. The case oftime-varying state dimension is considered. Input-output stability of all truncated balanced realizations is also proven. The method is finally successfully applied to a high-order model.",

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AB - In this paper balanced truncation of linear time-varying systems is studied in discrete and continuous time. Based on relatively basic calculations with time-varying Lyapunov equations/inequalities we are able to derive both upper and lower error bounds for the truncated models. These results generalize well-known time-invariant formulas. The case oftime-varying state dimension is considered. Input-output stability of all truncated balanced realizations is also proven. The method is finally successfully applied to a high-order model.

KW - linear timevarying systems

KW - Balanced truncation

KW - error bound

KW - model reduction

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DO - 10.1109/TAC.2003.822862

M3 - Article

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JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

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Balanced truncation of linear time-varying systems

Abstract

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Free keywords

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