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ISS-Lyapunov functions for discontinuous discrete-time systems

Title data

Grüne, Lars ; Kellett, Christopher M.:
ISS-Lyapunov functions for discontinuous discrete-time systems.
Department of Mathematics, University of Bayreuth
In: IEEE Transactions on Automatic Control. Vol. 59 (2014) Issue 11 . - pp. 3098-3103.
ISSN 0018-9286
DOI: https://doi.org/10.1109/TAC.2014.2321667

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Abstract in another language

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: Article in a journal
Refereed: Yes
Additional notes: 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
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 14:43
Last Modified: 27 Apr 2015 14:43
URI: https://eref.uni-bayreuth.de/id/eprint/11282

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