ERef Bayreuth

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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
Bayreuth , 2014 . - 19 p.

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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:	Preprint, postprint
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:	18 Apr 2015 21:00
Last Modified:	20 Apr 2015 07:07
URI:	https://eref.uni-bayreuth.de/id/eprint/10503

Available Versions of this Item

ISS-Lyapunov functions for discontinuous discrete-time systems. (deposited 18 Apr 2015 21:00) [Currently Displayed]
- ISS-Lyapunov functions for discontinuous discrete-time systems. (deposited 27 Apr 2015 14:43)