Construction of time-varying ISS-Lyapunov Functions for Impulsive Systems
Abstract
Time-varying ISS-Lyapunov functions for impulsive systems provide a necessary and sufficient condition for ISS. This property makes them a more powerful tool for stability analysis than classical candidate ISS-Lyapunov functions providing only a sufficient ISS condition. Moreover, time-varying ISS-Lyapunov functions cover systems with simultaneous instability in continuous and discrete dynamics for which candidate ISS-Lyapunov functions remain inconclusive. The present paper links these two concepts by suggesting a method of constructing time-varying ISS-Lyapunov functions from candidate ISS-Lyapunov functions, thereby effectively combining the ease of construction of candidate ISS-Lyapunov functions with the guaranteed existence of time-varying ISS-Lyapunov functions.
Keywords
Cite
@article{arxiv.2203.08651,
title = {Construction of time-varying ISS-Lyapunov Functions for Impulsive Systems},
author = {Patrick Bachmann and Saeed Ahmed},
journal= {arXiv preprint arXiv:2203.08651},
year = {2026}
}