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ISS-Lyapunov functions for discontinuous discrete-time systems

URN to cite this document: urn:nbn:de:bvb:703-epub-2002-4

Title data

Grüne, Lars ; Kellett, Christopher M.:
ISS-Lyapunov functions for discontinuous discrete-time systems.
Department of Mathematics, University of Bayreuth
Bayreuth , 2014 . - 19 S.

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Abstract

Input-to-State Stability (ISS) and the ISS-Lyapunov function are useful tools for the analysis and design of nonlinear systems. 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 dissipative 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 function and provide a complete characterization of ISS-Lyapunov functions for discrete-time systems with discontinuous dynamics.

Further data

Item Type:	Preprint, postprint
Additional notes (visible to public):	erschienen in: IEEE Transactions on Automatic Control. Bd. 59 (2014) Heft 11 . - S. 3098-3103. DOI: https://doi.org/10.1109/TAC.2014.2321667 A preliminary version was published at the homepage of the first author in July 2013.
Keywords:	input-to-state stability (ISS); Lyapunov methods; discrete-time systems
DDC Subjects:	500 Science > 510 Mathematics
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
Language:	English
Originates at UBT:	Yes
URN:	urn:nbn:de:bvb:703-epub-2002-4
Date Deposited:	17 Apr 2015 07:21
Last Modified:	01 Jun 2021 09:11
URI:	https://epub.uni-bayreuth.de/id/eprint/2002

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