A set valued characterization of ISDS Lyapunov functions

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Grüne, Lars ; Saint-Pierre, Patrick:
A set valued characterization of ISDS Lyapunov functions.
Bayreuth , 2005

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Abstract

We use set valued analysis techniques in order to characterize Lyapunov functions for the input--to--state dynamical stability (ISDS) property, a quantitatively sharper but qualitatively equivalent variant of the well known input--to--state stability (ISS) property. We show that the epigraphs of minimal ISDS Lyapunov functions are invariance kernels of a suitable augmented differential inclusion. This identity provides theoretical insight into local ISDS properties and yields a basis for a numerical approximation of ISDS and ISS Lyapunov functions via set oriented numerical methods.