An invariance kernel representation of ISDS Lyapunov functions

Titelangaben

Grüne, Lars ; Saint-Pierre, Patrick:
An invariance kernel representation of ISDS Lyapunov functions.
In: Systems & Control Letters. Bd. 55 (2006) Heft 9 . - S. 736-745.
ISSN 1872-7956
DOI: https://doi.org/10.1016/j.sysconle.2006.02.003

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Abstract

We apply set valued analysis techniques in order to characterize the input--to--state dynamical stability (ISDS) property, a variant of the well known input--to--state stability (ISS) property. Using a suitable augmented differential inclusion we are able to characterize the epigraphs of minimal ISDS Lyapunov functions as invariance kernels. This characterization gives new insight into local ISDS properties and provides a basis for a numerical approximation of ISDS and ISS Lyapunov functions via set oriented numerical methods.