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Bounded power signal spaces for robust control and modeling
Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
Leeds University.
1999 (English)In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 37, no 1, p. 92-117Article in journal (Refereed) Published
Abstract [en]

The nonlinear space of signals allowing Wiener's generalized harmonic analysis (GHA), the linear bounded power signal spaces of Beurling, Marcinkiewicz, and Wiener, and a new linear bounded power space are studied from a control and systems theory perspective. Specifically, it is shown that the system power gain is given by the $H_\infty$ norm of the system transfer function in each of these spaces for a large class of (power) stable finite and infinite dimensional systems. The GHA setup is shown to possess several limitations for the purpose of robustness analysis which motivates the use of the other more general (nonstationary) signal spaces. The natural double-sided time axis versions of bounded power signal spaces are shown to break the symmetry between Hardy space $H_\infty$ methods and bounded power operators; e.g., the system transfer function being in $H_\infty$ does not imply that a causal-linear time-invariant (LTI) system is bounded as an operator on any of the double-sided versions of the studied bounded power signal spaces.

Place, publisher, year, edition, pages
1999. Vol. 37, no 1, p. 92-117
National Category
Control Engineering
Research subject
Control Engineering
Identifiers
URN: urn:nbn:se:ltu:diva-7765DOI: 10.1137/S0363012997316664Local ID: 62e897e0-91ff-11db-8975-000ea68e967bOAI: oai:DiVA.org:ltu-7765DiVA, id: diva2:980655
Note

Godkänd; 1999; 20061222 (ysko)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-02-06Bibliographically approved

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