Comparison of peak and RMS gains for discrete-time systems
type: Item
instance of: scholarly article
title: Comparison of peak and RMS gains for discrete-time systems
zbMATH Open document ID: 0644.93050
DOI: 10.1016/0167-6911(87)90002-8
author: B. George
published in: Systems \& Control Letters
publication date: 1987-01-01T00:00:00Z
review text: A convolution system can have a frequency response which is small for all frequencies, yet still greatly amplify the peaks of signals passing through it. For finite-dimensional systems, however, we establish the simple bound \(\| h\|_ 1\leq (2n+1)\| h\|_{H^{\infty}}\), where \(\| h\|_ 1\) is the peak gain of the system, \(\| h\|_{H^{\infty}}\) is the maximum frequency response of the system, and n its dimension. The same result for continuous-time systems is due to Gohberg and Doyle and it is mentioned in ``Robust control of multivariable and large scale systems'', Final Tech. Report, Honeywell Systems and Research Center, Minneapolis, MN (1985). The bound implies that \(H^{\infty}\)-optimal controllers, which minimize the maximum of some disturbance-to-error transfer function, cannot have very large peak gains from the disturbance to error.
Mathematics Subject Classification ID: 93D25
Mathematics Subject Classification ID: 42A85
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 30D55
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 93B50
zbMATH DE Number: 4051471
zbMATH Keywords: RMS gain
zbMATH Keywords: peak gain
zbMATH Keywords: \(H^{\infty }\)-optimal controllers
MaRDI profile type: Publication
full work available at URL: 0167-6911(87)90002-8
OpenAlex ID: W2024972569
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cites work: On H&lt;sup&gt;∞&lt;/sup&gt;-optimal sensitivity theory for SISO feedback systems
cites work: All optimal Hankel-norm approximations of linear multivariable systems and theirL,∞-error bounds†
cites work: Synthesis of minimum roundoff noise fixed point digital filters
cites work: Design of sensitivity and round-off noise optimal state-space discrete systems
cites work: Q3802944
cites work: Optimal rejection of persistent bounded disturbances
cites work: Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses
cites work: Feedback, minimax sensitivity, and optimal robustness
description: scientific article; zbMATH DE number 4051471