Jacob, B, Nabiullin, R, Partington, JR orcid.org/0000-0002-6738-3216 et al. (1 more author) (2018) Infinite-Dimensional Input-to-State Stability and Orlicz Spaces. SIAM Journal on Control and Optimization, 56 (2). pp. 868-889. ISSN 0363-0129
Abstract
In this work, the relation between input-to-state stability and integral input-to-state stability is studied for linear infinite-dimensional systems with an unbounded control operator. Although a special focus is laid on the case L∞, general function spaces are considered for the inputs. We show that integral input-to-state stability can be characterized in terms of input-to-state stability with respect to Orlicz spaces. Since we consider linear systems, the results can also be formulated in terms of admissibility. For parabolic diagonal systems with scalar inputs, both stability notions with respect to L∞ are equivalent.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018, Society for Industrial and Applied Mathematics. This is an author produced version of a paper published in SIAM Journal on Control and Optimization. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | input-to-state stability; integral input-to-state stability; C0-semigroup; admissibility; Orlicz spaces |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 03 Jan 2018 13:45 |
Last Modified: | 01 May 2018 20:26 |
Status: | Published |
Publisher: | Society for Industrial and Applied Mathematics |
Identification Number: | 10.1137/16M1099467 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:125700 |