Global converse Lyapunov theorems for infinite-dimensional systems

Titelangaben

Mironchenko, Andrii ; Wirth, Fabian:
Global converse Lyapunov theorems for infinite-dimensional systems.
University of California, Santa Barbara
In: IFAC-PapersOnLine. Bd. 49 (2016) Heft 18 . - S. 897-902.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2016.10.280

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Abstract

We show that existence of a non-coercive Lyapunov function is sufficient for uniform global asymptotic stability (UGAS) of infinite-dimensional systems with external disturbances provided an additional mild assumption is fulfilled. For UGAS infinite-dimensional systems with external disturbances we derive a novel ‘integral’ construction of non-coercive Lipschitz continuous Lyapunov functions. Finally, converse Lyapunov theorems are used in order to prove Lyapunov characterizations of input-to-state stability of infinite-dimensional systems.