An invariance kernel representation of ISDS Lyapunov functions

L. Grüne, P. Saint-Pierre: An invariance kernel representation of ISDS Lyapunov functions
Systems & Control Letters 55, 736 - 745, 2006

Smart-Link: http://www.elsevier.com/locate/sysconle
DOI: 10.1016/j.sysconle.2006.02.003
Keywords: input-to-state stability; invariance kernel; Lyapunov functions; set valued analysis; set oriented numerics
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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.

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