Title data
Grüne, Lars ; Kellett, Christopher M.:
Strong implicationform ISSLyapunov functions for discontinuous discretetime systems.
Department of Mathematics, University of Bayreuth
Bayreuth
,
2014


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Project information
Project title: 
Project's official title Project's id MarieCurie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO)" 264735SADCO ARC Future Fellowship FT1101000746 Humboldt Research Fellowship ohne Angabe 

Project financing: 
7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union AlexandervonHumboldt Foundation Australien Research Council (ARC) 
Abstract
InputtoState Stability (ISS) and the ISSLyapunov 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 eventbased control, lead to discontinuous discretetime dynamics, we investigate ISSLyapunov functions for such systems. ISSLyapunov functions were originally introduced in a socalled implicationform and, in many cases, this has been shown to be equivalent to an ISSLyapunov function of dissipationform. However, for discontinuous dynamics, we demonstrate via an example that this equivalence no longer holds. We therefore propose a stronger implicationform ISSLyapunov which reestablishes the equivalence to dissipationform ISSLyapunov functions and to the ISS property for discontinuous systems.