Upper and Lower Bounds for Approximation in the Gap Metric

Tryphon T. Georgiou; Malcolm C. Smith

doi:10.1109/9.222308

Upper and Lower Bounds for Approximation in the Gap Metric

Tryphon T. Georgiou
, Malcolm C. Smith

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

9 Scopus citations

Abstract

This note establishes upper and lower bounds for the closest approximant of degree k < n in the gap metric to a plant of degree n. The bounds are expressed in terms of the singular values of two Hankel operators defined from the symbol of the graph of the plant. The question of robust stability and performance of feedback systems is examined in the context of approximation of plant and controller in the gap metric.

Original language	English (US)
Pages (from-to)	946-951
Number of pages	6
Journal	IEEE Transactions on Automatic Control
Volume	38
Issue number	6
DOIs	https://doi.org/10.1109/9.222308
State	Published - Jun 1993
Externally published	Yes

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title = "Upper and Lower Bounds for Approximation in the Gap Metric",

abstract = "This note establishes upper and lower bounds for the closest approximant of degree k < n in the gap metric to a plant of degree n. The bounds are expressed in terms of the singular values of two Hankel operators defined from the symbol of the graph of the plant. The question of robust stability and performance of feedback systems is examined in the context of approximation of plant and controller in the gap metric.",

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AU - Smith, Malcolm C.

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AB - This note establishes upper and lower bounds for the closest approximant of degree k < n in the gap metric to a plant of degree n. The bounds are expressed in terms of the singular values of two Hankel operators defined from the symbol of the graph of the plant. The question of robust stability and performance of feedback systems is examined in the context of approximation of plant and controller in the gap metric.

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U2 - 10.1109/9.222308

DO - 10.1109/9.222308

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EP - 951

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 6

ER -

Upper and Lower Bounds for Approximation in the Gap Metric

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