Admissibility of Diagonal State-Delayed Systems with a One-Dimensional Input Space

Abstract

In this paper we investigate admissibility of the control operator B in a Hilbert space state-delayed dynamical system setting of the form z˙(t)=Az(t−τ)+Bu(t) , where A generates a diagonal semigroup and u is a scalar input function. Our approach is based on the Laplace embedding between L2 and the Hardy space. The sufficient conditions for infinite-time admissibility are stated in terms of eigenvalues of the generator and in terms of the control operator itself.

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Item Type:	Article
Authors/Creators:	Partington, JR https://orcid.org/0000-0002-6738-3216 Zawiski, R
Copyright, Publisher and Additional Information:	© The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Keywords:	Admissibility; State delay; Diagonal system; Reciprocal system
Dates:	Accepted: 5 March 2019 Published (online): 18 March 2019 Published: July 2019
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:	07 Mar 2019 11:33
Last Modified:	12 Jul 2019 11:51
Status:	Published
Publisher:	Springer International Publishing
Identification Number:	10.1007/s11785-019-00910-5
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:143352

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Admissibility of Diagonal State-Delayed Systems with a One-Dimensional Input Space

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