Construction of time-varying ISS-Lyapunov functions for impulsive systems

Titelangaben

Bachmann, Patrick ; Ahmed, Saeed:
Construction of time-varying ISS-Lyapunov functions for impulsive systems.
In: IFAC-PapersOnLine. Bd. 56 (2023) Heft 1 . - S. 1-6.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2023.02.001

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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.