A dual notion to BIBO stability

Felix Schwenninger; Alexander A. Wierzba

doi:10.1016/j.jmaa.2024.129156

A dual notion to BIBO stability

Felix Schwenninger, Alexander A. Wierzba^*

^*Corresponding author for this work

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

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Abstract

In this paper we consider BIBO stability of infinite-dimensional linear state-space systems and the related notion of L¹-to-L¹ input-output stability (abbreviated LILO). We show that in the case of finite-dimensional input and output spaces, both are equivalent and preserved under duality transformations. In the general case, neither of these properties is satisfied, but BIBO and LILO stability remain dual to each other.

Original language	English
Article number	129156
Number of pages	17
Journal	Journal of mathematical analysis and applications
Volume	545
Issue number	2
Early online date	11 Dec 2024
DOIs	https://doi.org/10.1016/j.jmaa.2024.129156
Publication status	E-pub ahead of print/First online - 11 Dec 2024

Keywords

UT-Hybrid-D

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10.1016/j.jmaa.2024.129156Licence: CC BY

ArticleFinal published version, 506 KBLicence: CC BY

Cite this

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abstract = "In this paper we consider BIBO stability of infinite-dimensional linear state-space systems and the related notion of L1-to-L1 input-output stability (abbreviated LILO). We show that in the case of finite-dimensional input and output spaces, both are equivalent and preserved under duality transformations. In the general case, neither of these properties is satisfied, but BIBO and LILO stability remain dual to each other.",

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AB - In this paper we consider BIBO stability of infinite-dimensional linear state-space systems and the related notion of L1-to-L1 input-output stability (abbreviated LILO). We show that in the case of finite-dimensional input and output spaces, both are equivalent and preserved under duality transformations. In the general case, neither of these properties is satisfied, but BIBO and LILO stability remain dual to each other.

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DO - 10.1016/j.jmaa.2024.129156

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