On vinnicombe metrics and the stability robustness of linear time-varying systems

Wynita M. Griggs; Alexander Lanzon; Brian D.O. Anderson

On vinnicombe metrics and the stability robustness of linear time-varying systems

Wynita M. Griggs, Alexander Lanzon, Brian D.O. Anderson

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other

Abstract

We present two novel approaches for obtaining stability robustness information about linear time-invariant systems with norm-bounded time-varying output multiplicative perturbations using Vinnicombe metrics. First, a time-varying Vinnicombe metric approximation between a nominal linear time-invariant system and the perturbed linear time-varying system is developed, and we show that a calculable tight upper bound may be placed on the approximation for a subclass of small, periodic output multiplicative errors. Second, we show that a worst-case time-invariant Vinnicombe metric may be used to obtain stability robustness information about the perturbed time-varying system.

Original language	English
Title of host publication	2004 5th Asian Control Conference
Publisher	IEEE, Institute of Electrical and Electronics Engineers
Pages	1459-1467
Number of pages	9
Volume	3
ISBN (Print)	0780388739
Publication status	Published - 2004
Externally published	Yes
Event	Asian Control Conference 2004 - Melbourne, Australia Duration: 20 Jul 2004 → 23 Jul 2004 Conference number: 5th

Conference

Conference	Asian Control Conference 2004
Abbreviated title	ASCC 2004
Country/Territory	Australia
City	Melbourne
Period	20/07/04 → 23/07/04

Cite this

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title = "On vinnicombe metrics and the stability robustness of linear time-varying systems",

abstract = "We present two novel approaches for obtaining stability robustness information about linear time-invariant systems with norm-bounded time-varying output multiplicative perturbations using Vinnicombe metrics. First, a time-varying Vinnicombe metric approximation between a nominal linear time-invariant system and the perturbed linear time-varying system is developed, and we show that a calculable tight upper bound may be placed on the approximation for a subclass of small, periodic output multiplicative errors. Second, we show that a worst-case time-invariant Vinnicombe metric may be used to obtain stability robustness information about the perturbed time-varying system.",

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T1 - On vinnicombe metrics and the stability robustness of linear time-varying systems

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AU - Lanzon, Alexander

AU - Anderson, Brian D.O.

N1 - Conference code: 5th

PY - 2004

Y1 - 2004

N2 - We present two novel approaches for obtaining stability robustness information about linear time-invariant systems with norm-bounded time-varying output multiplicative perturbations using Vinnicombe metrics. First, a time-varying Vinnicombe metric approximation between a nominal linear time-invariant system and the perturbed linear time-varying system is developed, and we show that a calculable tight upper bound may be placed on the approximation for a subclass of small, periodic output multiplicative errors. Second, we show that a worst-case time-invariant Vinnicombe metric may be used to obtain stability robustness information about the perturbed time-varying system.

AB - We present two novel approaches for obtaining stability robustness information about linear time-invariant systems with norm-bounded time-varying output multiplicative perturbations using Vinnicombe metrics. First, a time-varying Vinnicombe metric approximation between a nominal linear time-invariant system and the perturbed linear time-varying system is developed, and we show that a calculable tight upper bound may be placed on the approximation for a subclass of small, periodic output multiplicative errors. Second, we show that a worst-case time-invariant Vinnicombe metric may be used to obtain stability robustness information about the perturbed time-varying system.

UR - http://www.scopus.com/inward/record.url?scp=16244374967&partnerID=8YFLogxK

M3 - Conference Paper

AN - SCOPUS:16244374967

SN - 0780388739

VL - 3

SP - 1459

EP - 1467

BT - 2004 5th Asian Control Conference

PB - IEEE, Institute of Electrical and Electronics Engineers

T2 - Asian Control Conference 2004

Y2 - 20 July 2004 through 23 July 2004

ER -

On vinnicombe metrics and the stability robustness of linear time-varying systems

Abstract

Conference

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