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

12 Downloads (Pure)

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

Access to Document

10.1016/j.jmaa.2024.129156Licence: CC BY

ArticleFinal published version, 506 KBLicence: CC BY

1 Preprint

A dual notion to BIBO stability
Schwenninger, F. L. & Wierzba, A. A., 12 Aug 2024, ArXiv.org, 16 p.
Research output: Working paper › Preprint › Academic

Open Access
File

39 Downloads (Pure)

Cite this

@article{3814a9a15f924af3a3caf1119c042a08,

title = "A dual notion to BIBO stability",

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.",

keywords = "UT-Hybrid-D",

author = "Felix Schwenninger and Wierzba, {Alexander A.}",

year = "2024",

month = dec,

day = "11",

doi = "10.1016/j.jmaa.2024.129156",

language = "English",

volume = "545",

journal = "Journal of mathematical analysis and applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - A dual notion to BIBO stability

AU - Schwenninger, Felix

AU - Wierzba, Alexander A.

PY - 2024/12/11

Y1 - 2024/12/11

N2 - 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.

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.

KW - UT-Hybrid-D

U2 - 10.1016/j.jmaa.2024.129156

DO - 10.1016/j.jmaa.2024.129156

M3 - Article

SN - 0022-247X

VL - 545

JO - Journal of mathematical analysis and applications

JF - Journal of mathematical analysis and applications

IS - 2

M1 - 129156

ER -