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Strong implication-form ISS-Lyapunov functions for discontinuous discrete-time systems

Title data

Grüne, Lars ; Kellett, Christopher M.:
Strong implication-form ISS-Lyapunov functions for discontinuous discrete-time systems.
In: MTNS 2014 : Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems. - Groningen : University of Groningen , 2014 . - pp. 1023-1030
ISBN 978-90-367-6321-9

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Official URL: Volltext

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Project information

Project title:
Project's official titleProject's id
Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO)"264735-SADCO
ARC Future FellowshipFT1101000746
Humboldt Research Fellowshipohne Angabe

Project financing: 7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union
Australien Research Council (ARC)
Alexander-von-Humboldt Foundation

Abstract in another language

Input-to-State Stability (ISS) and the ISS-Lyapunov function have proved to be useful tools for the analysis and design of nonlinear systems in a variety of contexts. Motivated by the fact that many feedback control laws, such as model predictive control or event-based control, lead to discontinuous discrete-time dynamics, we investigate ISS-Lyapunov functions for such systems. ISS-Lyapunov functions were originally introduced in a so-called implication-form and, in many cases, this has been shown to be equivalent to an ISS-Lyapunov function of dissipation-form. However, for discontinuous dynamics, we demonstrate via an example that this equivalence no longer holds. We therefore propose a stronger implication-form ISS-Lyapunov which re-establishes the equivalence to dissipation-form ISS-Lyapunov functions and to the ISS property for discontinuous systems.

Further data

Item Type: Article in a book
Refereed: Yes
Additional notes: An extended version of this paper was submitted to the IEEE Transactions
on Automatic Control.
Keywords: input-to-state stability (ISS); Lyapunov functions; discrete-time systems
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne)
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 27 Apr 2015 13:18
Last Modified: 27 Apr 2015 13:18
URI: https://eref.uni-bayreuth.de/id/eprint/11268

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