Jacob, B, Mironchenko, A, Partington, JR orcid.org/0000-0002-6738-3216 et al. (1 more author) (2020) Non-coercive Lyapunov functions for input-to-state stability of infinite-dimensional systems. SIAM Journal on Control and Optimization, 58 (5). pp. 2952-2978. ISSN 0363-0129
Abstract
We consider an abstract class of infinite-dimensional dynamical systems with inputs. For this class the significance of noncoercive Lyapunov functions is analyzed. It is shown that the existence of such Lyapunov functions implies norm-to-integral input-to-state stability (ISS). This property in turn is equivalent to ISS, if the system has some sort of regularity. For a particular class of linear systems with unbounded admissible input operators, explicit constructions of noncoercive Lyapunov functions are provided. The theory is applied to a heat equation with Dirichlet boundary conditions.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 Society for Industrial and Applied Mathematics. This is an author produced version of a paper published in Siam Journal of Control and Optimization. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | infinite-dimensional systems, input-to-state stability, Lyapunov functions, nonlinear systems, linear systems |
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: | 08 Jul 2020 15:55 |
Last Modified: | 02 Nov 2020 10:44 |
Status: | Published |
Publisher: | Society for Industrial and Applied Mathematics |
Identification Number: | 10.1137/19M1297506 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:162986 |