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Closed-form expressions for the pure time delay in terms of the input and output Laguerre spectra
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control.ORCID iD: 0000-0002-6608-250x
2024 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 159, article id 111366Article in journal (Refereed) Published
Abstract [en]

The pure time delay operator is considered in continuous and discrete time under the assumption of the input signal being integrable (summable) with square. Then the input and the output signals are uniquely given by their Laguerre spectra. It is shown that a discrete convolution operator with polynomial Markov parameters constitutes a common description of the delay operator in the continuous and discrete case. Closed-form expressions for the delay value in terms of the output and input Laguerre spectra are derived. The expressions hold for any feasible value of the Laguerre parameter and can be utilized for e.g. building time-delay estimators that allow for non-persistent input. A simulation example is provided to illustrate the principle of Laguerre-domain time-delay modeling and analysis with perfect disturbance rejection.

Place, publisher, year, edition, pages
Elsevier, 2024. Vol. 159, article id 111366
Keywords [en]
Delay systems, Infinite-dimensional systems, Time-invariant systems
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:uu:diva-518033DOI: 10.1016/j.automatica.2023.111366ISI: 001106929700001OAI: oai:DiVA.org:uu-518033DiVA, id: diva2:1821021
Funder
Swedish Research Council, 2019-04451Available from: 2023-12-19 Created: 2023-12-19 Last updated: 2023-12-19Bibliographically approved

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Medvedev, Alexander

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