A set valued characterization of ISDS Lyapunov functions

L. Grüne, P. Saint-Pierre: A set valued characterization of ISDS Lyapunov functions
in: Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference (ECC2005), Sevilla, Spain, 2005, 4718 - 4723

Smart-Link: http://www.esi2.us.es/~cdcecc05/
DOI: 10.1109/CDC.2005.1582907
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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.

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