at Google ScholarTitle data
Ahmed, Saeed ; Bachmann, Patrick ; Trenn, Stephan:
Lyapunov characterization for ISS of impulsive switched systems.
Groningen, The Netherlands
,
2024
. - 15 p.
DOI: https://doi.org/10.48550/ARXIV.2410.22521
Abstract in another language
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.
Further data
| Item Type: | Preprint, postprint |
|---|---|
| Keywords: | ISS; switched systems; impulsive systems; Lyapunov methods; dwell time; leave time |
| Subject classification: | arXiv Subjects: eess.SY |
| Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Profile Fields > Advanced Fields > Nonlinear Dynamics |
| Result of work at the UBT: | No |
| DDC Subjects: | 500 Science > 510 Mathematics |
| Date Deposited: | 11 Mar 2025 08:01 |
| Last Modified: | 11 Mar 2025 08:01 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/92729 |