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Ahmed, Saeed ; Bachmann, Patrick ; Trenn, Stephan:
Lyapunov characterization for ISS of impulsive switched systems.
Groningen, The Netherlands
,
2024
. - 15 S.
DOI: https://doi.org/10.48550/ARXIV.2410.22521
Abstract
In this study, we investigate the ISS of impulsive switched systems that have modes with both stable and unstable flows. We assume that the switching signal satisfies mode-dependent average dwell and leave time conditions. To establish ISS conditions, we propose two types of time-varying ISS-Lyapunov functions: one that is non-decreasing and another one that is decreasing. Our research proves that the existence of either of these ISS-Lyapunov functions is a necessary and sufficient condition for ISS. We also present a technique for constructing a decreasing ISS-Lyapunov function from a non-decreasing one, which is useful for its own sake. Our findings also have added value to previous research that only studied sufficient conditions for ISS, as our results apply to a broader class of systems. This is because we impose less restrictive dwell and leave time constraints on the switching signal and our ISS-Lyapunov functions are time-varying with general nonlinear conditions imposed on them. Moreover, we provide a method to guarantee the ISS of a particular class of impulsive switched systems when the switching signal is unknown.
Weitere Angaben
| Publikationsform: | Preprint, Postprint |
|---|---|
| Keywords: | ISS; switched systems; impulsive systems; Lyapunov methods; dwell time; leave time |
| Fachklassifikationen: | arXiv Subjects: eess.SY |
| Institutionen der Universität: | Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik) Profilfelder > Advanced Fields > Nichtlineare Dynamik |
| Titel an der UBT entstanden: | Nein |
| Themengebiete aus DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Eingestellt am: | 11 Mär 2025 08:01 |
| Letzte Änderung: | 11 Mär 2025 08:01 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/92729 |