An invariance kernel representation of ISDS Lyapunov functions

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Grüne, Lars ; Saint-Pierre, Patrick:
An invariance kernel representation of ISDS Lyapunov functions.
Bayreuth , 2005

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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.