Lyapunov characterization of input-to-state stability for a class of impulsive systems

Titelangaben

Bachmann, Patrick ; Ahmed, Saeed ; Bajcinca, Naim:
Lyapunov characterization of input-to-state stability for a class of impulsive systems.
In: IEEE Transactions on Automatic Control. Bd. 69 (2024) Heft 10 . - S. 6996-7003.
ISSN 1558-2523
DOI: https://doi.org/10.1109/tac.2024.3392636

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Abstract

We prove that the existence of an input-to-state stability (ISS)-Lyapunov function is a necessary and sufficient condition for the input-to-state stability of a class of impulsive systems over Banach spaces. A key feature of our work is that it employs time-varying ISS-Lyapunov functions as opposed to candidate ISS-Lyapunov functions, which also makes it possible to conclude ISS of impulsive systems with unstable continuous and discrete dynamics.