A dual notion to BIBO stability

Felix L. Schwenninger; Alexander A. Wierzba

doi:10.48550/arXiv.2408.06313

A dual notion to BIBO stability

Felix L. Schwenninger
, Alexander A. Wierzba

Research output: Working paper › Preprint › Academic

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Abstract

In this paper we consider BIBO stability of infinite-dimensional linear state-space systems and the related notion of $L^1$-to-$L^1$ 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
Publisher	ArXiv.org
Number of pages	16
DOIs	https://doi.org/10.48550/arXiv.2408.06313
Publication status	Published - 12 Aug 2024

Keywords

math.OC
math.FA
93D25, 93C05, 47D06, 93C20

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10.48550/arXiv.2408.06313Licence: Other

PreprintFinal published version, 254 KBLicence: Other

A dual notion to BIBO stability
Schwenninger, F. & Wierzba, A. A., 15 May 2025, In: Journal of mathematical analysis and applications. 545, 2, 17 p., 129156.
Research output: Contribution to journal › Article › Academic › peer-review

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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 \$L\textasciicircum{}1\$-to-\$L\textasciicircum{}1\$ 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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