Upper and Lower Bounds for Approximation in the Gap Metric

Tryphon T. Georgiou, Malcolm C. Smith

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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 languageEnglish (US)
Pages (from-to)946-951
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number6
StatePublished - Jun 1993
Externally publishedYes


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